Design of an Enhanced Access Point to Optimize TCP Performance in Wi-Fi Hotspot Networks

Transcription

1 Design of an Enhanced Access Point to Optimize TCP Performance in Wi-Fi Hotspot Networks Raffaele Bruno, Marco Conti, Enrico Gregori Institute of Informatics and Telematics (IIT) Italian National Research Council (CNR) Via G. Moruzzi 1, Pisa - ITALY firstname.lastname@iit.cnr.it 1 Abstract In the last years, the number of Wi-Fi hotspots at public venues has undergone a substantial growth, promoting the WLAN technologies as the ubiquitous solution to provide high-speed wireless connectivity in public areas. However, the adoption of a random access CSMA-based paradigm for the MAC protocol makes difficult to ensure high throughput and a fair allocation of radio resources in based WLANs. In this paper we evaluate extensively via simulations the interaction between the flow control mechanisms implemented at the TCP layer and the contention avoidance techniques used at the MAC layer. We conducted our study considering initially M wireless stations performing downloads from the Internet. From our results, we observed that the TCP downlink throughput is not limited by the collision events, but by the inability of the MAC protocol to assign a higher chance of accessing the channel to the base station. We propose a simple and easy to implement modification of the base station s behavior with the purpose of increasing the TCP throughput reducing useless MAC protocol overheads. With our scheme, the base station is allowed to transmit periodically bursts of data frames towards the mobile hosts. We design a resource allocation protocol aimed at maximizing the success probability of the uplink transmissions by dynamically adapting the burst length to the collision probability estimated by the base station. By its design, our scheme is also beneficial to achieve a fairer allocation of the channel bandwidth among the downlink and uplink flows, and among TCP and UDP flows. Simulation results confirm both the improvement in the TCP downlink throughput and the reduction of system unfairness. Index Terms Hotspot, Multiple Access Protocol (MAC), IEEE 82.11, TCP, resource allocation, performance evaluation I. INTRODUCTION In the last five years, since the 82.11b standard has been released by the Institute of Electrical and Electronics Engineers (IEEE) as the standard for Wireless Local Area Networks (WLANs) [1], we have witnessed the massive deployment of wireless access networks and the upsurge in the number of wireless users. Current Wi-Fi (acronym for Wireless-Fidelity) wireless LANs based on the 82.11b technology provide data rates up to 11 Mbps, but forthcoming extensions of this technology, as the a and g versions [2], [3], are expected to rise the data rates up to tens of Mbps. Thus, WLAN technologies can effectively open up the widespread deployment of wireless Internet applications since they can be used as an ubiquitous networking platform providing wireless cost-effective network access: i) at home for private customers; ii) to SOHO (Small Office/Home Office) customers; iii) to enterprises;

2 2 and iv) in public environments. Infrastructure-based wireless networks deployed in public places, such as cafes, retail shops, convention centers, airports and other areas where people can benefit from a seamless public access to the Internet, are commonly known as hotspot networks. Currently the telecommunication market of hotspot networks is relatively small but it is expected to undergo a substantial growth in the coming years. Indeed, wireless Internet service providers are rapidly setting up a large number of Wi-Fi hotspots at public venues. However, there are key business and technical issues that should be solved to led to the acceptance of WLAN technologies as the ubiquitous solution to provide high-speed wireless connectivity in public areas with large number of users. These problems include, but are not limited to, billing and provisioning models, authentication and security, interoperability with different wireless access networks [4]. However, at least in the first stage of the hotspot networks deployment, the most crucial concerns for the service providers and the hotspot operators are expected to be: i) how to provide an efficient support for services with a wide variety of QoS requirements; ii) how to guarantee a true high-speed connection to the Internet as the number of users increases; and iii) how to efficiently manage and allocate the channel access among the wireless stations. In this paper, the last issue is the main focus of our research. In wireless LANs, the Medium Access Control (MAC) protocol is the main element in determining the efficiency of allocating the channel bandwidth among the wireless stations. One of the major obstacles to ensure high throughput and a fair allocation of radio resources in based WLANs is the adoption of a random access CSMA-based scheme for the MAC protocol, which allows unconstrained movement of mobile hosts, but doesn t provide guarantees on the stations throughput. An extensive literature of analytical models characterizing the channel utilization in based networks is available [5] [7]. All these studies consider saturated stations, i.e, hosts with transmission queues never empty, which transmit to randomly selected destinations. However, these studies cannot be easily applied to the hotspot networks. Specifically, if we consider a typical hotspot installation, the mobile stations are accessing the Internet through the base station that acts as aggregator of the wireless stations traffic 1. Therefore, the base station is the bottleneck node that affects the overall performance of the network. Moreover, the majority of the Internet applications are based on the TCP protocol, which traffic is rate controlled, thus we cannot generally assume that mobile senders and receivers are saturated. Other researchers have addressed the issue of characterizing the behavior of UDP protocol [8], [9] and TCP protocol [1] [12] over an WLAN through simulations and experimentations. Generally, the studies on the TCP performance are mainly focused on the fairness among TCP flows. In particular, these works analyze the unfairness caused by channel unavailability [1], buffer size availability at the base station [11], and coexistence of high-speed and low-speed wireless stations [12]. In this paper we address the study of the interaction between the flow control mechanisms implemented at the TCP layer and the contention avoidance techniques used at the MAC layer. Specifically, we have initially evaluated through simulations the throughput performance in the presence of M wireless stations performing downloads from the Internet. This is a remarkably traffic configuration in hotspot networks as indicated by large trace-based studies conducted in real local-area wireless networks [13], [14]. These measurements campaigns found out that most users 1 In this paper the terms base station and access point are used with the same meaning, while the mobile hosts are referred to as the wireless stations.

3 3 exploit the network for web-surfing and session oriented-activities (i.e., applications based on the TCP protocol), and that the incoming traffic dominates outgoing traffic. We conducted our study considering the system from the MAC protocol perspective, in order to gain a better understanding on the causes of severe performance limitations shown by the TCP traffic in hotspot networks. From our results, we observe that the collision probability on the uplink transmissions is negligible because most of the time the wireless stations are inactive, i.e., without frames to transmit to the base station. Specifically, a few wireless stations on average compete with the access point for the channel access even with a large number of mobile receivers involved in downloads. This observation is fundamental because it confirms that the TCP throughput is not limited by the collisions events at the MAC layer, but by the inability of the MAC protocol to assign a higher chance of accessing the channel to the base station. One of the main contributions of this paper is the proposal of a simple and easy to implement modification of the base station s behavior in order to improve the TCP downlink throughput. Our solution aims at reducing the useless MAC protocol overheads that precede TCP data transmissions and increasing the activity of wireless stations acting as TCP receivers. More specifically, we propose a solution that doesn t require any change in the network cards of wireless stations, which continue to be fully compliant. With our scheme, the base station is allowed to transmit periodically bursts of data frames towards the mobile hosts with the purpose of increasing the wireless stations activity. The base station monitors the collision probability of the uplink transmissions and selects the burst length most appropriate to the current contention level. In order to determine the burst length that maximizes the system efficiency we develop an analytical study to compute the collision probability that ensures the maximum success rate of uplink transmissions. By its design, our scheme is also beneficial to achieve a fairer allocation of the channel bandwidth among the downlink and uplink flows, and among TCP and UDP flows. In particular, our results show that mobile receivers with a low activity are significantly hindered in the presence of mobile senders. Since our scheme has the effect of increasing the mobile receivers activity, the TCP downlink flows are more protected from both UDP and TCP uplink flows. We have evaluated the performance of our scheme by comparison against the performance obtained using the standard MAC protocol. The numerical results confirm both the improvement in the TCP downlink throughputs and the beneficial effect on the system fairness. The rest of the paper is organized as follows. In Section II we present the simulation study of the throughput performance of TCP and UDP flows over hotspot networks. In Section III we analytically characterize the system efficiency in terms of the success rate of uplink transmissions. In Section IV we describe our proposed scheme. Section V presents numerical results to evaluate the performance of our scheme. In Section VI we discuss ongoing activities. Section VII concludes the paper. II. STUDY OF THE THROUGHPUT PERFORMANCE IN 82.11b HOTSPOT NETWORKS The performance of 82.11b-based WLANs has been extensively studied, and experimental measurements have been conducted on commercial products to evaluate the UDP [8], [9] and TCP [11], [12] throughputs. The experimentations on test beds are fundamental to highlight the issues of a technology, however these tests are usually limited to observing the behavior of transport layer protocols. Furthermore, the measurements may be affected by several factors, including the link quality and the implementation details of network interface card (NIC), which

4 4 may preclude the possibility of conducting a rigorous study. Finally, the manufacturers don t make available to the application layer the status of relevant MAC protocol parameters, as the instantaneous backoff value, the transmission buffer s overflows, the collision events and so on. Therefore, in this work we have conducted simulations to gain a better understanding of the MAC protocol operations in the case of mixed traffic scenarios with both UDP and TCP flows. This study is aimed at investigating i) the impact of multiple TCP flows on the contention level that the MAC protocol has to deal with; ii) the interaction between the flow control mechanism implemented at the TCP layer and the contention avoidance technique used at the MAC layer; and iii) the interaction between upstream and downstream traffic flows in a typical hotspot network. The performance evaluation has been carried out with a discrete-event simulator in which we assume an ideal channel condition with no transmission errors 2. The TCP version considered is the TCP-Reno, the most worldwide adopted commercial TCP implementation [17]. If not otherwise stated, the TCP senders are asymptotic sources, i.e., they have always a data packet ready to be transmitted (ftp-like traffic), while the UDP senders are CBR traffic sources. We set the TCP receiver window to 2 16 bytes, that is the default value in most TCP implementations. If not otherwise stated, the buffers are assumed to be 1 data frames long both at the base station and the wireless stations. For the details on the MAC protocol overheads the reader is referred to the IEEE 82.11b specification [1]. For each experiment, we conducted 5 simulation runs, each simulating 5 seconds of transmissions. A. Multiple TCP/UDP Downlink Flows The first network scenario we studied is a hotspot network with only downstream traffic flows, i.e., the mobile stations download traffic through the access point, but there aren t active uplink connections. In this scenario we have considered two traffic configurations. In the first one, the downstream traffic is constituted by M TCP downlink connections and each station is the receiver of a different connection. In this case we vary the number of wireless stations in the network. In the second configuration, the downstream traffic is constituted by one UDP flow and we vary the offered load (OL) of the CBR sender. This study has a twofold purpose. Firstly, we want to identify the maximum throughput the base station can attain, a measure that will be used as reference value in the other scenarios we consider. Secondly, we want to investigate the impact of the TCP flow control mechanisms over the MAC protocol behavior. Specifically, by increasing the network population we increase the contention suffered by the base station transmissions due to the TCP acknowledgment traffic generated by the mobile receivers. However, the MAC protocol attempts to control the growth in the network contention, by exploiting its own collision avoidance mechanisms, i.e., increasing exponentially the contention windows used during the backoff procedure. On the other hand, the rate of TCP ACKs depends on the amount of TCP data traffic the base station succeeds in delivering to the TCP receivers. Therefore, a comprehensive simulation study is needed to understand the complex interaction between the TCP feedback-based behavior and the MAC layer, and to find out possible inefficiencies of the channel allocation scheme adopted by the MAC protocol. 2 Our simulator strictly follows the MAC protocol and TCP specifications. More details on the simulation tool can be found in [15] and [16].

5 5 7 6 l= 536B l=124b l=146b 6 5 l= 536B l=124b l=146b Throughput (Kbps) Throughput (Kbps) Offred Load (Kbps) M (a) UDP case (b) TCP case Fig. 1. Aggregate throughput for a hotspot network with only downstream traffic flows. Figure 1(a) and Figure 1(b) show the throughput achieved by the base station in the UDP and TCP case 3, respectively. The curves refer to the use of different payload sizes l. A payload l = 146 corresponds to a MT U of 15 bytes, the maximum packet size in Ethernet networks. It can be observed from our results that: i) the UDP throughput increases as far as the offered load saturates the wireless link; ii) the TCP throughput is slightly affected by the number of stations, in fact the throughput measured with 2 wireless stations is about 96% of the one with a single wireless station; and iii) the maximum TCP throughput is significantly lower than the maximum UDP throughput. In order to better understand the TCP behavior, it is useful to identify the three main reasons that could limit the TCP throughput. The first one is the overhead introduced both by the MAC protocol (interframe guard times, headers, control packets, etc.) and the TCP protocol (acknowledgment traffic, retransmissions, etc.). The second reason is the packet losses due to buffer overflows at the base station. The last one is the collisions due to the contention at the MAC layer. The almost negligible dependence of the TCP throughput on the number of wireless stations suggests that the TCP downlink throughput is mostly limited by the protocols overheads rather than the collision events at the MAC layer. To confirm this observation in the following we analyze in depth the MAC protocol operations. First of all, we consider the average contention window used by the access point and the wireless stations, which is a relevant parameter to characterize the MAC protocol behavior. Indeed, the larger is the average contention window the longer is the average time waited by the stations before attempting a transmission. Our simulations indicate that the average contention window is slightly above 32 slots, independently of the M value, thus both the access point and the wireless stations experience a few collisions, on average. To explain why the TCP traffic suffers a low number of collisions, we have estimated the average contention level in the network as the average number of wireless stations that have at least one TCP ACK to transmit after the base station s transmissions, henceforth indicated as active wireless stations. From our results, we observed that the average number of active stations slightly increases by increasing the hotspot population size, rising from.78 for 3 In the TCP case we consider the aggregate throughput, i.e., the sum of the throughputs of the single connections.

6 6 M = 1 to.95 for M = 2. To justify this counter-intuitive result we should consider how the TCP flow control mechanisms operate. Specifically, the wireless stations are the TCP receivers, therefore they can have a new TCP ACK to transmit to the base station only after the reception of TCP data packets from the base station. Consequently, the more traffic the base station sends to the wireless stations the more wireless stations become active. However, the larger is the number of active wireless stations the lower is the probability that the access point can experience a successful transmission because the random access scheme employed by the MAC protocol assigns to all the stations the same probability to access the channel. For this reason, the wireless stations tend to empty their transmissions buffers and to become inactive. This interaction between the traffic sent by the access point and the traffic replied back to the access point by the wireless stations, operates as an intrinsic closed-loop control that stabilizes the network, limiting the contention level to a few stations on average. To conclude the study of this scenario, in Figures 2 we show a snapshot of a wireless station s buffer occupancy. These results well summarize the previous considerations on wireless stations activity. In particular, Figure 2(a) 3 Receiver1 TCP pk 2 Receiver1 TCP pk 2 # TCP ACK 1 # TCP ACK Time (seconds) Time (seconds) (a) M = 1 (b) M = 2 Fig. 2. Snapshots of buffer occupancy at the station 1 for a hotspot with (a) 1 station and (b) 2 stations. and Figure 2(b) show the number of TCP ACKs queued in one wireless station s buffer in the case of a hotspot network with a single TCP flow and 2 TCP flows, respectively. It is straightforward to notice that not all the packet reception events cause the generation of a new TCP ACK, due to the Delayed ACK technique [17]. Furthermore, a few TCP ACKs are queued in the wireless stations, and even when there is a single TCP flow, the station s buffer is often empty. During our simulations we find out that the station s buffer is empty on average for the 21% of the time in the case M = 1. All these phenomena are further exacerbated when the hotspot population increases. When there are 2 TCP flows, each wireless station s buffer is empty on average for the 95% of the time. B. Mixed TCP/UDP Downlink and Uplink Flows The results presented so far show that the TCP downlink flows cannot saturate the wireless stations. This behavior depends heavily on the MAC protocol. Specifically, the basic access scheme employs a random access paradigm that assigns the same transmission probability to the base station and wireless stations. Basically, our

7 7 results indicate that the wireless stations are inactive most of the time when they behave as TCP receivers. This observation leads us to identify two main weaknesses in the way the base station manages the channel bandwidth. The first shortcoming is the following: if the access point isn t capable of delivering TCP data packets towards the mobile receivers at a sufficient pace, the TCP connections could slow down. We analyze more formally this aspect in the next section. The second issue is worth pointing out is the inability of the base station to ensure fairness in the presence of upstream flows. In particular, since the mobile receivers have a low activity, the presence of mobile senders could significantly hinder the TCP downlink connections. Although downstream traffic dominates upstream traffic, it is possible that there are transient conditions where the upstream traffic cannot be neglected, for instance when a single user begins a video-streaming application (i.e., UDP traffic) with a destination located outside the hotspot. In order to evaluate the impact on TCP downlink throughput of uplink flows, we have performed an extensive simulation study, considering different traffic configurations. In the following we describe the results of this simulation study. In particular, we will discuss why the unfairness between uplink and downlink flows is exacerbated if the wireless stations that are the TCP receivers, are inactive most of the time. 5 4 TCP - l= 536B UDP - l= 536B TCP - l=124b UDP - l=124b TCP - l=146b UDP - l=146b 5 4 TCP - l= 536B UDP - l= 536B TCP - l=124b UDP - l=124b TCP - l=146b UDP - l=146b Throughput (Kbps) 3 2 Throughput (Kbps) CBR (Kbps) CBR (Kbps) (a) r = 1% (b) r = 5% Fig. 3. TCP and UDP throughput versus the CBR offered load. In order to illustrate the unfairness issue in the presence of upload and downloads, we start considering a network scenario where the downstream traffic is constituted by TCP flows, while the upstream traffic comes from UDP sources. Let us denote with r the ratio between the number of uplink and downlink connections. For the sake of clarity, we assume that a wireless station is either the sender of UDP packets or the receiver of TCP packets. In the following we consider two traffic configurations. In the first one we have 1 TCP downlink flows and the ratio r is 1% (i.e., a single UDP uplink flow). In the second configuration we maintain the same number of TCP downlink connections, but we increase the ratio r to 5% (i.e., 5 UDP uplink flows). In both cases we investigate the fairness properties by increasing the offered load of the CBR sources. The results are shown in Figure 3(a) and Figure 3(b). This is well-known that the type of fairness the MAC protocol tries to ensure is a per station fairness, such that all the wireless stations achieve the same throughput 4. However, the allocation of the channel 4 This statement holds when all the wireless stations are asymptotic traffic sources.

8 TCP DW- l= 536B TCP UP - l= 536B TCP DW - l=124b TCP UP - l=124b TCP DW - l=146b TCP UP - l=146b Throughput (Kbps) 2 15 Throughput (Kbps) TCP DW- l= 536B TCP UP - l= 536B TCP DW - l=124b 5 TCP UP - l=124b TCP DW - l=146b TCP UP - l=146b # downstream flows / 1 upstream flow # downstream/upstream flows (a) r = 1/M (b) r = 1% Fig. 4. Comparison of TCP uplink and downlink throughputs as a function of the number of flows. bandwidth clearly indicates that the wireless stations that act as TCP receivers don t contribute significantly to the channel occupation. For instance in the first case, when r = 1%, the single UDP flow competes for the channel bandwidth with the access point and with other 1 wireless stations that are the receivers of the TCP downlink flows. However, the TCP receivers are inactive most of the time, therefore the UDP flow shares almost equally the channel with the base station. Our intuition is that the unfairness condition could be made less sever if the base station could deliver more TCP data traffic to the wireless stations such that they will be more frequently in an active state. The last network scenario we present in this section is formed by multiple TCP uplink and downlink flows. In this case the TCP uplink connections contribute to the contention on the uplink transmissions interfering with the TCP acknowledgment traffic of the mobile receivers. Furthermore, the TCP acknowledgment traffic of the uplink connections occupies buffer space at the base station, thus interfering with the TCP downlink data traffic. As well explained in [11], a loss of an acknowledgment packet due to buffer overflows at the base station hasn t a significant impact on the TCP uplink connections. Instead, the loss of a TCP data packet considerably affects the TCP downlink flows due to the TCP congestion avoidance behavior. Figure 4(a) and Figure 4(b) shows the TCP downlink and TCP uplink throughputs as a function of the number M of TCP downlink flows in the case of r = 1/M (i.e., a single TCP uplink flow) and r = 1% (i.e., the same number of TCP downlink and uplink flows), respectively. These results were obtained by considering a fixed buffer space at the base station equal to 15 KBytes 5. In the configuration with one TCP uplink flow, the results show that the TCP downlink throughput is higher than the TCP uplink throughput. However, the portion of channel bandwidth the TCP downlink flows gain is nearly independent of the number of TCP downlink flows. Hence, the unfairness increases almost linearly with the number of flows. In the case of r = 1%, we observe that as soon as the number of flows is greater than two, the downstream traffic suffers a significant unfairness, becoming the downlink throughput up to 8 times lower than the uplink throughput. It is worth pointing out that the unfairness among TCP flows is less critical than the unfairness in case of mixed 5 This buffer size is equal to 1 packets with a 146-bytes long payload.

9 9 scenarios with TCP and UDP flows. Specifically, there are many simple solutions to ensure fair access to TCP downlink and TCP uplink flows. One possible solution is to increase the base station s buffer space, reducing the probability of having buffer overflows. Another solution is to reduce the TCP sender window as proposed in [11]. However, the UDP behavior is independent of both the buffer availability at the base station and the TCP behavior, therefore different solutions should be envisioned. III. MODELING THE MAC PROTOCOL EFFICIENCY The results discussed in the previous section suggest that some shortcomings of the MAC protocol the inefficient utilization of the channel resources due to the high protocol overheads, the unfair bandwidth allocation of downlink and uplink flows could be alleviated if the base station is capable of increasing the activity of the wireless stations that act as TCP receivers. However, we should operate carefully when increasing the activity of the wireless stations because we also raise the contention level in the network, which could result in an unacceptable increase of the collision probability. Therefore, before designing a resource allocation policy that improve the system efficiency we have: i) to introduce a formal definition of the system efficiency; ii) to design a procedure to measure it; and iii) to identify the operating conditions that maximize the system efficiency. In this work we adopted the concept of success rate to evaluate the system efficiency. Specifically, we observe the channel during a fixed number w of virtual slots, and we compute the success rate as the ratio between the number of successful slots and the overall duration of this window of w virtual slots. We use the same notation followed by Bianchi in [6] where the virtual slots can be: i) empty slots with duration t slot, when no stations are transmitting; ii) collision slots with duration T c, when two or more stations collide; and iii) successful slots with duration T s, when a single station is transmitting. Therefore, the virtual slots haven t the same duration. We can formally define the success rate, hereafter indicated as ρ, as follows ρ = N s N i t slot + N s T s + N c T c, (1) where N i, N s and N c are the number of idle slots, successes and collisions during the w virtual slots. To approximate the ρ value, in this paper we don t consider the standard binary exponential backoff, but a modified MAC protocol adopting a fixed backoff size w. This assumption leads to a significant simplification of the problem formulation, and it is motivated by the observation that in the case of TCP downlink flows there are a few collisions, therefore the stations use the minimum contention window CW MIN. Consequently, our results, although approximated, can be applied to optimize the performance of TCP downstream traffic. The problem we address in this section is to determine the number m of contending wireless stations that should be active after the base station s transmissions, in order to maximize the success rate in a window of w virtual slots. To achieve our goal we have to calculate how many of these w virtual slots will be idle slots, how many will be collision slots and how many will be successful slots. Henceforth, given that there are m active wireless, we indicate the number of successful slots that will be observed during a window of w virtual slots as E[N s ] w m, the number of collisions as E[N c ] w m, and the number of idle slots as E[N i ] w m. First of all we need to express the probability, given m active stations, that a virtual slot is a success, say P s (w, m), a collision that involves k

10 1 stations, say P c (w, m, k), or an idle slot, say P i (w, m). Following the approach used in [5], and indicating with p w the probability that a wireless station is transmitting in a slot conditioned to the fact that it will try to access the channel within the following w virtual slots, we can write P s (w, m) = m p w (1 p w ) m 1, P c (w, m, k) = P i (w, m) = (1 p w ) m. ( ) m p k w (1 p w ) m k, k (2a) (2b) (2c) Since we have assumed a fixed backoff size w, the m active stations will uniformly try to access the channel within the next w virtual slots, therefore p w = 1/w. By exploiting formulas (2), the following Lemma defines recursive algorithms to derive E[N s ] w m, E[N c ] w m and E[N i ] w m. Lemma 1: If m active wireless stations uniformly try a transmission attempt during w consecutive virtual slots, the number of successful, collision and idle slots during these w virtual slots can be approximated as follows: m E[N s ] w m P s (w, m){1+e[n s ] w 1 m 1 }+ P c (w, m, k)e[n s ] w 1 m k +P i(w, m)e[n s ] w 1 m, (3a) k=2 k=2 m E[N c ] w m P s(w, m)e[n c ] w 1 m 1 + P c (w, m, k){1+e[n c ] w 1 m k }+P i(w, m)e[n c ] w 1 m, (3b) m E[N i ] w m P s(w, m)e[n i ] w 1 m 1 + P c (w, m, k)e[n i ] w 1 m k +P i(w, m) {1+E[N i ] w 1 m }, (3c) k=2 Proof: We prove the formula (3a) because the others are obtained by using the same line of reasoning. To derive E[N s ] w m we have to observe the system for w consecutive virtual slots. Let us consider the first virtual slot. It will be a successful slot with probability P s (w, m). In this case the counter of successful slots is incremented by one. After this successful transmission the number of active stations is m 1, and they will attempt a transmission in the following w 1 virtual slots. Therefore, the remaining successful slots are E[N s ] w 1 m 1. On the other hand, the first virtual slot could be a collision slot that involve k stations with probability P c (w, m, k). To simplify the analysis, we assume that these k colliding stations will not contribute to the successes or to the collisions in the remaining w 1 virtual slots 6. Therefore, in the following w 1 virtual slots, m k stations will attempt a transmission attempt, resulting in E[N s ] w 1 m k successful slots. Finally, the first virtual slot can be an idle slot with probability P i (w, m). In this case we have still m stations attempting a transmission in the following w 1 virtual slots, contributing to the number of successful slots with E[N s ] w 1 m. To derive the E[N c ] w m and the E[N i ] w m values we follow the same reasoning. The only difference is that we have to count collision events and idle slots, respectively. 6 This assumption leads to underestimate the number of stations that try to access the channel, hence providing an overestimate of the success rate.

11 11 Lemma 1 can be used to calculate the success rate as a function of the m value, hence determining the m value that maximizes it. Unfortunately, the recursive algorithm requires a considerable computational cost as m increases. To solve this problem we have also developed an efficient iterative procedure to compute formulas (3). This procedure is based on the construction of three matrixes with (w +1) rows and (m+1) columns, S = {s i,j }, C = {c i,j } and I = {i i,j }, whose elements are defined, respectively, as: s i,j = E[N s ] i j, c i,j = E[N c ] i j and i i,j = E[N i ] i j, for i =, 1, 2,..., w and j =, 1, 2,..., m. The matrices elements are computed by exploiting the formulas derived in Lemma 1. For instance, the s i,j is s i,j = P s (i, j) {1 + s i 1,j 1 } + m P c (i, j, k) s i 1,j k + P i (i, j) s i 1,j. (4) k=2 Hence, the quantities defined in formulas (3) are the last element on the matrixes diagonals. Furthermore, once we have calculate E[N s ] w m, we have for free the E[N s] w j for j m, that are given by the last row of S. Clearly, the same holds for C and I. By examination of equation (4), it is straightforward to notice that the s i,j element depends only on the elements of the first j columns of the previous row. Therefore, to apply the iterative procedure we need only to know a priori the elements {s 1,j, s i, } {c 1,j, c i, } and {i 1,j, i i, } for i =, 1, 2,..., w and j =, 1, 2,..., m 7. Let us begin from the first couple. The index i indicates the size of the window where all the j wireless station will try a transmission attempt. Hence, i = 1 implies that all the j stations will access the channel, thus we can count a successful slot only for j = 1. On the other hand if j = we cannot have transmissions. To summarize s i, = for i =, 1, 2,..., n, s 1,j = { 1 if j = 1 if j = 2,..., m. (5) In the case of collisions the reasoning is clearly the opposite. In fact, if i = 1 we have to count a collision for j > 1. Hence c i, = for i =, 1, 2,..., w, c 1,j = { if j = 1 1 if j = 2,..., m. (6) The case of idle slots is different. If i = 1 and j >, there will be at least a transmission attempt in that slot, therefore we cannot count idle slots. If j = we cannot have transmissions, and all the remaining i virtual slots will be idle slots. Hence i i, = i for i =, 1, 2,..., w, i 1,j = for j = 1, 2,..., m. (7) Using the initial conditions derived in formulas (5), (6) and (7), we are finally able to compute the quantities defined in Lemma 1. Figure 5(a) shows the success rate as a function of the number m of active stations, for different contention windows w. To evaluate the duration of successful slots and collisions slots we have considered stations sending 4-bytes long packets 8, and introduced all the MAC protocol overheads. From the shown results it is easily to derive the m corresponding to the maximum success rate (the black dots in the plots). The numerical results 7 It is straightforward to note that s,j = c,j = i,j = for j =, 1, 2,..., m. 8 This is the typical size of the TCP ACK.

12 w=32 w=16 w=8 w= L=4 L=25 L=5 L=1 L=1 ρ (succ per msec) ρ (succ per msec) m m (a) (b) Fig. 5. Success rate as a function of m for (a) several contention window size w and (b) several packet sizes. indicate that for all the w values analyzed the success rate is maximized by a number m of stations such that m min(2, w/4). This is a not-intuitive condition, and we identified it by exploiting our analytical study. Further studies of this nice property are an ongoing activity beyond the scope of this paper. It is worth pointing out that this property depends on the specific setting of the MAC protocol overheads and packet size. It is straightforward to observe that increasing the contention window w, the MAC protocol can ensure the same success rate to a larger hotspot population. To evaluate the impact of the packet size on the ρ value, in Figure 5(b) we report the success rate as a function of the data frame payload, keeping w = 32. From our results we can observe that the success rate depends significantly on the data payload size, however, the m value doesn t show the same dependency. In particular, the m value ranges in the interval [5,..., 8] varying the payload size from 15 bytes to 4 bytes. To validate our modeling approach, in Figure 6 we compare the success rate as estimated exploiting our analytical model, and the success rate measured through simulations of an based WLANs. The shown results refer to CW MIN equal to 32 or 16 slots, which are the default values for the MAC protocol [1]. The analysis shows a good correspondence with the simulation. In particular, the approximated model well describe the system behavior for small network populations. From the numerical results, we can notice that there is a not negligible deviation of the simulations from the analysis for large network populations. However, these differences don t affect the significance of our results, because the model aims at providing a way to determine the optimal contention level given the CW MIN value, rather than to exactly describe the system behavior for generic network configurations. IV. RESOURCE ALLOCATION STRATEGIES TO MAXIMIZE SYSTEM EFFICIENCY In this section we propose a simple and easy to implement enhancement of the MAC protocol in order to improve the system efficiency in the hotspot network scenarios considered in this paper. We can identify two main concerns when proposing modifications of the MAC layer. The first one is that the extended MAC protocol could require hardware modifications to be implemented, which is infeasible given the wide deployment of network interface cards (NICs) compliant with the standard IEEE Nevertheless, it is not infeasible to propose

13 w=32 - analysis w=32 - simulation w=16 - analysis w=16 - simulation 1.2 ρ (succ per msec) m Fig. 6. Success rate: analysis versus simulation. extensions to the standard MAC layer, which involve only firmware upgrades or LLC-layer modifications in the network cards of the base station, without changing the network cards installed in the mobile stations. From the hotspot operators perspective, indeed, the cost of upgrading the software in the base stations could be worthy, if it results in a more efficient management of the channel resources without requiring the users to change their network cards. The second concern is related to the compatibility requirements that any protocol extension should fulfill. It is desirable that the protocol modifications are designed in such a way that the behavior of the standard protocol is not hampered by the operations of the enhanced one. In other words, mixed scenarios should be supported where standard and modified network cards safely inter-operate without resulting in performance degradations of the mobile hosts using network cards compliant to the standard protocol. The solution we propose takes into account both of these concerns as we will explain in the following. As briefly outlined in the introduction, a considerable research activity has been focused on improving the MAC protocol efficiency in terms of the maximum achievable channel utilization. This objective was mainly pursued by modifying the standard backoff procedure to minimize the collision probability (see [5], [7], [18] [2] and references herein). A wise choice of the contention window, which should be dynamically tuned according to the network configuration (i.e., the number of stations in the network) and traffic conditions (i.e., the distribution of the message lengths), can significantly increase the system throughput. However, these policies are not effective in the hotspot configuration, in particular for the TCP downlink traffic, since the collision events are not the most relevant cause of throughput limitation. From our results, we observed that a more effective way to improve the system efficiency is reducing the useless MAC protocol overheads that precede TCP data packets transmissions, and increasing the activity of wireless stations acting as TCP receivers. These two objectives can be jointly achieved allowing the base station to transmit multiple frames in a burst. Each frame within the burst will be separated by a DIFS interval (i.e., it is transmitted adopting a null backoff) and independently acknowledged by the wireless stations. By exploiting the analytical results developed in Section III, the base station can compute the burst length such as to optimize the contention level suffered by the wireless stations on the uplink transmissions. Specifically, during each backoff interval that precedes a burst transmission, the base station counts all the transmission attempts, either successes or collisions, performed by the wireless stations using the standard sensing activity. This information

14 14 is used to estimate the collision probability of wireless stations transmissions, which is compared against the optimal collision probability p to decide whether the base station should increase or reduce the burst length. The optimal collision probability p is defined as the collision probability that should be measured in a network with m active wireless stations. It is important to notice that we decided to use the equivalent notion of optimal collision probability p instead of controlling directly the number of active stations, because an estimation of the number of backlogged wireless station is proved to be expensive, difficult to obtain, and subject to significant error, especially in high contention situations [19]. Before describing the algorithm we use to dynamically compute the burst length, it is worth discussing how the solution that we designed differs from other proposals that try to assign higher priority to the base station s transmissions. Firstly, we can notice that the feature of multiple frame transmissions is introduced also in the EDCF access scheme of the current 82.11e draft [21]. However, the base station can fully exploit the EDCF bursting capability if all the wireless station forming the hotspot network use NICs compliant to the 82.11e standard. One of the most important guiding principles we followed when proposing our solution is to avoid any hardware and software change in the NICs of the wireless stations. To allow the base station to use a null backoff for the frame transmissions within the burst is easy to implement because, although the binary truncated exponential backoff algorithm distribution is usually hardwired in the NIC, the distribution parameters can be set in the NIC driver. Thus, to implement a null backoff it is sufficient to set to zero the maximum contention window value in the base stations NICs. From the wireless stations perspective, the MAC protocol holds its correctness because they can continue to operate with a standard backoff. Finally, it is worth pointing out that the optional access scheme proposed by the IEEE standard, the Point Coordination Function (PCF) [1], is also based on the idea of assigning an higher priority to the transmissions of a Point Coordinator (PC) 9. However, significant differences can be identified between our approach and the PCF. In the PCF each PC s transmission is followed by the stations replies. When the station contacted by the PC has no traffic to send either to the PC or to another station, it is mandated to deliver a null packet, further reducing the protocol efficiency. Basically, the PCF is a polling scheme where the PC transmits in a contention-free manner and decides the order the stations are allowed to send frames: stations that are not polled are blocked by the PC. In our scheme the base station contend with the wireless stations for the channel access and the transmission of its burst. Furthermore, the base station doesn t control the wireless stations transmissions. Indeed, following the base station s burst transmissions, the wireless stations will regulate the channel access according to the standard DCF contention-based scheme. In order to explain the algorithm we propose to select the burst length that optimizes the network contention level, in Figure 7 we show the collision probability as a function of the number m of active stations. We remind that the p value is the collision probability that should be observed if m wireless stations are active. Hence, the base station can assume that when it measures a collision probability greater than p the uplink is heavy loaded by the wireless stations transmissions. In this case, the base station should significantly decrease the burst length b to quickly reduce the network contention level. On the other hand, if the measured collision probability is lower 9 As indicated by the standard, the PC shall reside in the access point, but it is an option for the access point of be able to become the PC.

15 HEAVY LOAD.25 P coll.2 NORMAL LOAD p * LIGHT LOAD.5*p * m Fig. 7. Collision probability versus the number of active stations. than p, the base station can safely increase the burst length. One critical question that arises is, how fast can the base station increase the burst length? Again we use the collision probability to decide: if the collision probability is significantly low (in Figure 7 we choose half of the p value to identify this condition) the base station deems the uplink as lightly loaded and increase the burst length by adding the factor b 1, otherwise the uplink is normally loaded and the burst length is increased by adding the factor b 2, with b 1 > b 2. The complete algorithm description is the following b i+1 = b i + b 1 p colli.5 p (light load conditions) b i+1 = b i + b 2.5 p < p colli p (normal load conditions) b i+1 = max{b i /2, 1} p colli > p (heavy load conditions), (8) where, p colli is the estimate of the average collision probability computed at the base station after transmitting the i-th burst, say b i, and b i+1 is the length of the next burst. In case of heavy load conditions we decided to halve the burst length. To halve the amount of traffic we inject in the network in case of high contention is a common practice in the Internet protocols that implement congestion control schemes (see, for instance, the TCP protocol that halves the congestion window after realizing that a packet loss is occurred). It is worth pointing out that we select the minimum burst length as one data-frame long to guarantee that the base station behaves as using the standard MAC protocol when there is a condition of persistent heavy load in the network. Specifically, if the base station selects b i+1 = 1, it will transmit a single data frame and then it generates a new random backoff period. This is the same behavior of a base station implementing a standard DCF access scheme. The need of adaptively tuning the burst length is motivated considering the random access scheme, which the MAC protocol relies on. In fact, even if the average collision probability is low (the p value indicates that less than the 3% of transmission attempts collide when ρ is maximal), the stochastic selection of the backoff intervals can cause transient congestion conditions that our algorithm can quickly recover. As described previously, the base station estimates the collision probability by counting the number of collisions occurring between two consecutive burst transmissions. However, this is an instantaneous measure that could be highly variable, while our algorithm requires an average measure of the collision probability. In order to use a

16 16 reliable estimation of the average collision probability, the base station filters the instantaneous measures using a moving-window filter. Specifically, p colli = α p colli 1 + (1 α) p coll, where p coll is the collision probability measured after the burst b i, and the coefficient α (α < 1) determines the filter memory. After a transition from normal to heavy load conditions, which causes the half of the burst length, the p coll estimator is reset to avoid multiple consecutive halves of the burst length. It is worth pointing out that the moving-window filters are commonly used to estimate network quantities [7]. V. NUMERICAL RESULTS In this section we evaluate the effectiveness of our resource allocation strategy by comparing the performance obtained by a legacy base station, i.e., executing the standard MAC protocol, against the performance of a hotspot managed by a base station implementing the scheme described in Section IV. In the following plots we label the results related to the standard MAC protocol as STD-MAC, while the results obtained using our scheme are labeled as B-MAC. We investigate the behavior of our proposed scheme in the same network and traffic conditions considered in Section II in order to confirm the improvements with respect to the standard protocol. In the simulations, we set α =.95, which implies that the filter memory is twenty samples. If not otherwise stated the numerical results were obtained using a packet payload size l of 536 bytes, both for TCP and UDP traffic. Simulations were also conducted considering larger packet sizes as done in Section II. We obtained similar results that are therefore omitted. A. Multiple TCP Downlink Flows First of all we consider the network scenario with only TCP downlink flows which performance, in the case of a legacy base station, are shown in Figure 1(b). As discussed in Section II-A, on average less than one wireless station has at least a TCP ACK to transmit after a base station s transmission. Allowing the base station to deliver bursts of TCP data packets could have a twofold benefit: 1) we reduce the MAC protocol overheads associated to the transmission of TCP data packets; and 2) we increase the number of active wireless stations present in the network after the base station s burst transmissions. Since the generation of the TCP data packets is controlled by the rate the acknowledgment traffic is received by the TCP senders, a larger number of active wireless stations could also increase the rate new TCP data packets are produced. Figure 8 shows the average throughput achieved by the base station when it implements either the standard MAC protocol or employs our resource allocation policy. From our results, we observe that the aggregate TCP downlink throughput can increase up to the 15% using our scheme. It is worth pointing out that our solution doesn t require that the base station knows the number of open TCP connections, or the number of wireless stations. Indeed, the base station has to monitor only the collision probability of uplink transmissions. Generally, knowing the number of active TCP connections could be difficult because some open connections may be actually idle.