Throughput Analysis of UDP and TCP Flows in IEEE b WLANs: A Simple Model and its Validation

Transcription

1 Throughput Analysis of UDP and TCP Flows in IEEE 82.11b WLANs: A Simple Model and its Validation Raffaele Bruno, Marco Conti, Enrico Gregori Italian National Research Council (CNR) IIT Institute Via G. Moruzzi, Pisa, Italy firstname.lastname@iit.cnr.it Abstract In this paper we present a simple analytical model to estimate the throughput performance in IEEE WLANs, in which inelastic traffic competes with elastic traffic. In the considered wireless network the inelastic traffic is composed of asymptotic UDP uplink flows, while the elastic traffic consists of multiple persistent TCP uplink and downlink connections. We show that it is not necessary to precisely characterize the steady-state distribution of the network contention level in order to derive the throughput performance, because the overall TCP traffic can be equivalently modeled as two saturated flows. Starting from this finding, we develop an approximate model to evaluate the throughput of the UDP and TCP connections. Comparison with simulation results demonstrates that our approximate model is accurate in predicting the TCP and UDP throughput performance over a wide range of network and traffic configurations. 1 Introduction The last few years have seen an exceptional growth of the Wireless Local Area Network (WLAN) industry, with the substantial increase in the number of wireless users and applications. This growth was due, in large part, to the availability of inexpensive and highly interoperable network solutions based on the IEEE 82.11b standard [1], and to the growing trend of providing built-in wireless network cards into mobile computing platforms. Today, the attention of the industry and service providers is turning to deploying WLANs also over public places, or hot spots, such as cafes, retail shops, convention centers, airports and so on, from which people can benefit from a seamless public access to M. Conti s and E. Gregori s work was partially supported by the Italian Ministry for Education and Scientific Research (MIUR) in the framework of the FIRB-PERF project. R. Bruno s work was supported by the MIUR in the framework of the FIRB-VICOM project. the Internet. However, there are several business and technological challenges that have to be addressed to make public WLANs a global network infrastructure [2]. In particular, as the number of users increases and new emerging applications appear, the capability of ensuring minimum level of quality of service (QoS) to the users, in terms of guaranteed throughput, end-to-end delay bounds, etc., is one of the most crucial concerns for the service providers and the hot spot operators. In order to design adaptive resource management and bandwidth provisioning schemes it is important to have a clear understanding of which are the limitations of such networks in terms of scalability and efficiency, and how the resource availability depends on the traffic characteristics and users behaviors. The aim of this paper is to present a simple analytical model in order to evaluate the hot spot throughput performance in the presence of multiple TCP and UDP flows, which will be useful to guide the network design and dimensioning process. The hot spot networks rely on a shared wireless channel, therefore the behavior of the medium access control (MAC) protocol, and the overheads introduced by the MAC protocol to perform its coordination tasks, are fundamental factors in determining the efficiency of the channel access. For this reason, our analysis will specifically focus on modeling the MAC protocol operations. The MAC protocol provides as basic access method the Distributed Coordination Function (DCF), which is based on a CSMA/CA scheme using a slotted binary exponential backoff (BEB) 1. In the literature, it is widely recognized that the backoff protocol plays a crucial role in achieving a high aggregate throughput and a fair allocation of channel bandwidth to stations [1]. As a consequence, a considerable attention has been given within the research community to the modeling of the backoff mechanism to derive the maximum channel utilization achievable by the MAC protocol in different network conditions and 1 We assume that the reader is familiar with the IEEE MAC protocol. The reader is referred to [1] for the standard specification and [9] for a survey on the basic mechanisms used in the wireless MAC protocols.

2 configurations, e.g., [12, 3, 8, 17, 5, 15, 4] and references herein. These analytical studies have highlighted that the standard backoff algorithm significantly degrades the channel utilization in conditions of high contention, i.e., with a large number of stations, because this policy has to pay the cost of a collision to increase the backoff time when the network is congested. However, these previous results cannot be directly applied to hot spot networks because they were derived assuming inelastic traffic, which does not adapt its sending rate to the available channel bandwidth. Specifically, almost all the above mentioned papers assumed that the stations operate in asymptotic conditions, i.e., considering sources with an unlimited amount of data to send. In the case of inelastic traffic, the asymptotic conditions imply that the stations have always in their transmission queues a packet ready for transmission, i.e., are saturated. Moreover, it is usually assumed a uniform traffic distribution, i.e., each frame transmitted by a node is destined to another randomly selected node. To precisely model the hot spot network performance in presence of both TCP and UDP flows is necessary to relax, or modify, several assumptions usually adopted to derive the saturation throughput of based wireless networks. First of all, from a network perspective, a hot spot is an infrastructure-based network in which the mobile users access the network services through a base station or access point (AP). As a consequence, the traffic is not uniformly distributed over the stations in the network, but all the frames are sent to/delivered from the AP, which behaves as traffic aggregator. Hence, the AP is the real bottleneck of the network throughput, affecting and limiting the performance of the wireless stations. Furthermore, when considering the TCP traffic, we must take into account its elastic behavior. In fact, the TCP sending rate is regulated through a window-based flow control protocol that avoids continuous packet transmissions. According to the flow control techniques employed by the TCP to limit the transmission rate at the source [16], wireless stations that are the receivers of TCP sessions will have feedback traffic (i.e., TCP acknowledgment packets) to transmit to the AP depending on the number of TCP data packets they receive from the AP. Similarly, wireless stations that are the senders of TCP sessions will have TCP data packets to transmit depending on the pace of TCP acknowledgment packets received from the AP. As a consequence, the complex interaction between the contention avoidance part of the MAC protocol, and the closed-loop nature of TCP, induces a bursty TCP behavior with the TCP senders (or the TCP receivers) that could be frequently in idle state, without data (or acknowledgment) packets to transmit. Thus, the fact that the TCP senders operate in asymptotic conditions (i.e., with an infinite amount of data to send) does not imply that their transmission queues are saturated. As a consequence, the correct characterization of the TCP behavior could require an accurate modeling of the distribution of the number n b of backlogged stations in the network. To the best of the authors knowledge a few pioneering attempts have been recently made to model the interaction between TCP and MAC in hot spot networks [15, 13, 6]. However, these works lack completeness in one way or the other. The authors of [15] analyzed the TCP throughput as a function of the AP s buffer availability, highlighting that packet losses at the AP can induce severe unfairness between TCP uplink and donwlink connections. In [13], approximate expressions are derived for the TCP throughput in the case of multiple competing connections, either longlived or short-lived, identifying lower and upper bounds for the TCP throughput. In our previous paper [6] we developed an accurate analytical model to express the throughput of persistent TCP downlink and uplink connections, under the assumption of TCP advertised window equal to one. In this paper we step forward with respect to our previous work [6] because we consider the competition of multiple TCP downlink and uplink connections (i.e., elastic traffic), with UDP uplink flows (i.e., inelastic traffic). We will show that it is not necessary to precisely characterize the steady-state distribution of the number of backlogged wireless stations in the network in order to derive the throughput expressions. Indeed, an equivalent saturated network can be used to estimate the TCP and UDP throughput performance, in which the overall TCP traffic is modeled as two saturated traffic flows. Comparison with simulation results validates our analysis: the observed behavior shows a good match with the model predictions in all the considered network configurations. Exploiting the proposed analysis, we will show two relevant results: i) the aggregate TCP throughput, when inelastic traffic is not present, is almost independent of the number of wireless stations in the network because the average network backlog is negligibly affected by the number of TCP flows; ii) the presence of inelastic traffic, such as the UDP traffic, negatively affects the throughput of elastic traffic, such as the TCP traffic, inducing severe unfairness. The remaining of this paper is organized as follows. Section 2 introduces the system model. In Section 3 we discuss how to approximate the average network contention level. In Section 4 we develop the analytical model to compute the throughput of competing TCP and UDP flows. The comparison between analytical and simulations results, validating the model is reported in Section 5. Finally, Section 6 discusses on future research directions. 2 System Model We consider a hot spot network formed by n mobile users connected to an AP through an ideal wireless channel, i.e.,

3 not affected by channel errors. Let us assume that n d 1 wireless stations are the receivers of TCP downlink connections opened between the AP and the mobile users, while n u 1 wireless stations are the senders of TCP uplink connections opened between the mobile users and the AP, and the remaining n 2 = n n d 1 nu 1 wireless stations are the sources of UDP uplink flows destined to the AP. Hence, the number of TCP flows in the network is n 1 = n d 1 + nu 1. Figure 1 depicts the network configuration we considered in our work. Each wireless station is involved in a single longlived TCP session, i.e., a persistent TCP connection with an unlimited amount of data to send. Similarly the UDP traffic is assumed to be asymptotic, i.e., the UDP source has always a packet ready to be transmitted. For the sake of simplicity, in our model we assume that TCP and UDP flows generate data packets of fixed payload size equal to l T bytes, while the TCP acknowledgment packets have payload size equal to l A bytes. However, our mathematical framework can be straightforwardly extended to accommodate a general packet size distribution. In order to make analytically tractable the problem of modeling the interaction of elastic traffic (i.e., TCP) and inelastic traffic (i.e., UDP) with the DCF access scheme, we have adopted some simplifying assumptions, which will be introduced and motivated in the remaining of this section. Our model of the Figure 1. Network configurations considered in this paper. MAC protocol behavior is based on the assumption that the devices access the wireless slotted channel adopting a p- persistent IEEE 82.11b protocol [8]. This implies that a device uses a backoff interval sampled from a geometric distribution with parameter p. In [8], it was proved that by setting p = 1/(E[B] + 1) (where E[B] is the average backoff time of the standard protocol 2 ), the p-persistent IEEE model provides an accurate approximation (at least from a capacity analysis standpoint) of the IEEE protocol behavior. In the later sections we will discuss how 2 Note that E[B] is related to the average contention window size, E[CW ], through the relationship E[B] = (E[CW ] 1)/2 (see Lemma 2 in [8]). to estimate the p value in the specific network and traffic configurations considered in this paper. As far as the TCP evolution is concerned, we assume that: (i) the transmission buffers at the AP and wireless stations are large enough to ensure that no packets are lost due to buffer overflows; (ii) the retransmission timers at the TCP senders are long enough to avoid timeout expirations and useless retransmissions of TCP data packets; (iii) the receiver advertised window W is equal to one for all the TCP connections; and (iv) each TCP data packet is acknowledged separately, that is the delayed-ack mechanism [16] is disabled. Assumption (i) implies that the system is well dimensioned to avoid packet losses due to congestion on the wireless channel. This is reasonable considering that in hot spot networks the shared radio channel and the high protocol overheads introduced by the DCF access scheme are the main bottlenecks for the TCP performance. Furthermore, it is quite common to consider short Round Trip Times (RTTs) in this kind of high speed networks [14], such that no retransmission timeouts occur as assumed in point (ii) above. It is worth noting that the same assumptions were also adopted in previous papers addressing the problem of modeling TCP traffic in hot spot networks [6, 13]. Since no TCP data-packet losses and timeout expirations occur, the congestion window increases up to reach, after a transient phase, the advertised window W value, which is the flow control imposed by the TCP receivers. Under the assumptions (i), (ii) and (iv) above, for the i th TCP connection (with i = 1,..., n) the sum of the number X tcp (i) of TCP data packets queued in the transmission buffer of the sender (i.e., the AP for downlink connections or the mobile user for the uplink connections) and the number X ack (i) of TCP acknowledgment packets in the transmission buffer of the receiver (i.e., the mobile user for downlink connections or the AP for the uplink connections) is strictly equal to W at any time instant. For this reason, assumption (iii) above implies that X tcp (i) + X ack (i)=1. Under this assumption we can precisely compute the average number of backlogged wireless stations, as it will be explained in Section 3. Regarding assumption (iii), it is worth remarking that in [13] it was analytically studied the impact of the W value on the throughput performance for a single TCP connection. The authors of [13] proved that the maximum congestion window size has a negligible impact on the connection throughout. Furthermore, the throughout improvement for long-lived TCP connections due to W > 1 reduces as the number of TCP connections increases. For this reason, we claim that under the assumption W =1 the proposed model provides a useful insight of the real system behavior. Finally, it is worth pointing out that we have assumed that the delayed-ack mechanism is disabled for the sake of simplicity, however, our model can be easily extended to take into account the delayed-ack interval, as

4 better explained in the following section. 3 Approximating the number of backlogged wireless stations In a previous paper [6], we formulated a stochastic model to characterize the process n b (t), representing the number of backlogged wireless stations considering the case n 2 = (i.e., no UDP traffic), in which the time instant t corresponds to a generic AP s successful transmission 3. Using the p-persistent assumption, we proved that the n b (t) process can be modeled as a discrete-time Markov chain. Thus, the stationary probability Π k (with k = 1,..., n 1 ) of having n b = k active wireless stations at the time instant t is the steady-state probability of the chain, namely, Π k = lim t P r{n b (t) = k}. To derive the transition probabilities of this Markov chain, we exploited the assumption that for the i th TCP connection, it holds that X tcp (i)+x ack (i) = 1, as explained in Section 2. Specifically, for each TCP connection at most one TCP acknowledgment packet (for mobile TCP receivers) or TCP data packet (for mobile TCP senders) is queued in the wireless station s transmission buffer. Under these conditions, we obtained that Π k = 1 (k 1)! Π 1 k = 1, 2,..., n 1 (1) where Π 1 is equal to 1/ [ n k=1 1 (k 1)! ]. Therefore, the average number E[n b ] of active stations after an AP s successful transmission can be computed as: E[n b ] = n k Π(k). (2) k=1 Formula (1) holds in the case the delayed ACK mechanism is disabled. According to this mechanism, a TCP receiver will generate a new acknowledgment only after receiving d TCP data packets (unless the delay timer expires). The standard delayed ACK technique [16] suggest to use d = 2, i.e., to send an ACK every 2 received data packets, and in any case no later than 5 ms after the arrival of the first unacknowledged packet. This implies that with probability (d 1)/d no acknowledgment will be sent by the TCP receiver when a new TCP data packets is received (assuming that the delay timers never expire). As a consequence, the Markov chain describing the n b (t) evolution should be modified to take into account the fact that an AP s transmission does not always result in the activation of a new wireless station. However, this modification requires only standard probabilistic considerations. We assume d = 1 in 3 The details of the model are not reported here due to space constraints. The interested reader is referred to [7]. this paper, for the sake of simplicity and to make easier explanations of the observed TCP behaviors. In our previous paper [6], it was also derived the following proposition. Proposition 1 It holds that E[n b ] 2. The relationship E[n b ] = 2 is asymptotically valid, i.e., it holds when n. The graph in Figure 2 compares the average number of backlogged stations measured through discrete-event simulations with the predictions of the model, as given in formula (2). Since the distribution of the network backlog is independent of the n d 1 and n u 1 values, the figure shows results referring to the network scenario with n d 1 = x and n u 1 =. From the results, we can note that our proposed model slightly overestimates the average network backlog. Moreover, the findings of Proposition 1 are confirmed because the average network backlog is lower than two wireless stations. From the shown results, we can derive a very important observation: the interaction between the closedloop nature of the TCP control and the MAC contention avoidance scheme precludes the persistent TCP connections from saturating the wireless stations acting as TCP senders (or as TCP receivers). This is a radically different behav- E[n b ] analysis simulation Figure 2. Comparison of model predictions and observed behavior for the E[n b ] value in the network scenario with n d 1 = x, nu 1 = and n 2 =. ior when compared to the one shown by the UDP traffic. In fact, asymptotic UDP flows always saturate the source (i.e., the transmission queues of these stations are always non-empty) because the packet generation is not limited by any flow control mechanism. We argue that the presence of UDP flows will further interfere with the TCP traffic, increasing the burstiness of the TCP flows behavior. For this reason, we believe that it is not necessary to develop a full x

5 model to characterize the evolution of the TCP flows in the presence of asymptotic UDP traffic. Indeed, the contribution of the TCP flows to the network contention level can be approximated assuming that the overall TCP traffic is generated by two saturated stations, one modeling the traffic generated by the AP, and the other modeling the traffic of the wireless stations that are either TCP receivers or TCP senders. As a consequence, the original modeling problem is equivalent to consider a saturated network formed by ñ = n stations, in which each station immediately has a packet available for transmission, after the completion of each successful transmission. In the next section we will develop and validate closed-form throughput expressions of for this equivalent network. 4 Throughput Analysis Let ρ mac be the average MAC channel utilization considering a fixed number ñ = n of contending saturated stations that use a constant probability p to decide to transmit in a randomly chosen time slot. The MAC channel utilization is defined as the fraction of channel time used to successfully transmit frame payload bits at the MAC layer. Let us assume that the data rate used to transmit the MAC frames is r bytes/s. In [8], it was proved that the ρ mac value can be computed observing the system between two consecutive transmission attempts 4. However, in [8] the closedform expression for the ρ mac value was derived in the case of stations generating frames according to the same frame size distribution. On the contrary, in our model we have three different types of saturated nodes. The first node type is represented by n 2 wireless stations, hereafter denoted as S u, generating UDP traffic. As discussed in Section 2 we assume constant UDP-packet sizes. For this reason, denoting with F Su (l) the probability that the size of a generic S u s packet payload is lower than or equal to l bytes, it is straightforward to derive that F Su (l) = 1 for l l T. The second node type corresponds to the saturated AP. We derive F AP (l), i.e., the probability that the size of a generic AP s packet payload transmission is lower than or equal to l bytes, considering that the AP generates TCP data packets for the n d 1 TCP downlink flows and TCP acknowledgments for the n u 1 TCP uplink flows. Hence, it holds that: l < l A F AP (l) = n u 1 /n 1 l A l < l T. (3) 1 l l T The third node type corresponds to a saturated wireless station, hereafter denoted as S t, which models the overall TCP traffic generated by the real wireless stations that act either 4 We denote the time between two consecutive transmission attempts as virtual transmission time T v. as TCP receivers or as TCP senders. Considering that the equivalent S t station generates TCP acknowledgments for the n d 1 TCP downlink flows and TCP data packets for the nu 1 TCP uplink flows, the probability that the size of a generic S t s packet payload transmission is lower than or equal to l bytes, i.e., F St (l), can be expressed as: l < l A F St (l) = n d 1/n 1 l A l < l T. (4) 1 l l T The generic MAC frame is formed by adding to the MAC frame payload the PHY and MAC headers, while the MAC frame payload is constituted of the packet payoad, the IP header and the transport protocol header (either TCP or UDP). To compute the ρ mac value, let us analyze what can happen of each transmission attempt. Let P s denote the probability that a transmission attempt is a successful transmission. The P s value is given by the probability that exactly one station transmit on the channel, conditioned on the fact that at least one station transmits. Hence, it holds that: P s = ñp(1 p)ñ 1 1 (1 p)ñ. (5) Denoting with E[P ] the average transmission time of a frame payload, the average time interval in a virtual transmission time in which the channel is busy due to a successful transmission can be computed as P s E[P ]. On the other hand, it is straightforward to note that the probability P c that a transmission attempt is a collision is simply obtained as (1 P s ). Denoting with T idle the average idle period before a transmission attempt, with T s the average duration of a successful transmission, and with T c the average duration of a collision, the average virtual transmission time can be expressed as T v = T idle +P s T s +P c T c. Hence, the average MAC channel utilization can be computed as follows: ρ mac = P s E[P ] T idle +P c T c +P s T s. (6) To compute the ρ mac value for the specific traffic configurations considered for our network it is now necessary to specify the corresponding T c and T s values 5. Let τ be the maximum propagation time, t H the transmission time of PHY and MAC headers, and t ack the transmission time of the MAC-level acknowledgment. Considering the Basic Access method [1], we obtain: T s =2τ +DIF S+t H +E[P ]+SIF S+t ack, T c =τ +t H +E[P ]+EIF S, (7a) (7b) 5 The T idle value is independent of the traffic pattern. A closed-form expression for the T idle is provided in [8].

6 where E[P ] is the average transmission time of the longest frame payload involved in a collision. To completely define the average MAC channel utilization we have to derive closed-form expressions for the E[P ] and E[P ] values. The average duration of collisions and successful transmissions will depend on the distribution of the transmitted frame sizes as derived in formulas (3) and (4). In particular, the average transmission time of a frame payload is expressed as follows: E[P ] = H up /r+e[l AP ]P r(succ AP Succ)+ E[L Su ]P r(succ Su Succ)+ E[L St ]P r(succ St Succ), (8) where H up is the sum of the IP header size and the transport protocol (either TCP or UDP) header size, expressed in bytes, E[L x ] is the average transmission time of a packet payload sent by stations of type x (with x {AP, S t, S u }), and P r(succ x Succ) is the probability that a successful transmission is performed by a station of type x. Let L max the maximum packet payload size, the E[L x ] value can be computed as: r E[L x ] = L max l=1 l [F x (l) F x (l 1)]. (9) Finally, considering that the probability of performing a successful transmission attempt is independent of the station type, it is straightforward to derive that P r(succ AP Succ) and P r(succ St Succ) are both equal to 1/ñ, while P r(succ Su Succ) is equal to n 2 /ñ. In the general case, E[P ] = H up /r + E[L ], where E[L ] is the average transmission time of the longest packet payload involved in a collision. To compute the E[L ] value we should preliminary evaluate the P r(l = l i), i.e., the probability that the longest packet payload involved in a collision with i colliding packets is equal to l bytes. In fact, E[L ] can be written as L max r E[L ]= l l=1 ñ i=2 P r(l =l i) ( ) ñ i p i (1 p)ñ i 1 (1 p)ñ ñp(1, (1) p)ñ The packet payload size of each colliding packet depends on the type of station that generated the packet. For this reason, to facilitate the computation of the P r(l = l i) value we will differentiate between collisions that involve S u stations and collisions that does not involve S u stations. Thus, the P r(l =l i) can be written as: P r(l =l i) = P r(l =l i, Coll Su ) P r(coll Su i)+ P r(l =l i, Coll Su ) P r(coll Su i), (11) where P r(coll Su i) (P r(coll Su i)) is the probability that a collisions with i colliding packets involve (does not involve) a S u station. Using standard probabilistic arguments we derive that 1 i > 2 P r(coll Su i) = 2 ( 2 j)( n 2 i j). (12) j=1 i = 2 (ñ i) The P r(coll St i) value is simply obtained as (1 P r(coll St i)). Finally, it holds that (similar results can be found in [5]): P r(coll Su i)=f AP (l)f St (l) F AP (l 1)F St (l 1), (13a) P r(coll Su i)=[f Su (l)] i [F Su (l 1)] i. (13b) Now, we are able to derive the complete expressions of all the unknown terms in formula (6). 4.1 Closed-form expressions of TCP and UDP throughput Formula (6) provides the total channel utilization and, implicitly, the aggregate throughput. However, we need to distinguish between the throughout obtained by the TCP and UDP flows. Moreover, it is also important to properly compute the throughput of TCP uplink and downlink connections, in order to derive the system fairness properties. Let us define with ρ udp the channel utilization due to the UDP data transmission, with ρ u tcp the channel utilization due to the data packets transmitted in the TCP uplink connections, and with ρ d tcp the channel utilization due to the data packets transmitted in the TCP downlink connections. Considering that both UDP and TCP data packets have the same fixed size l T, it holds that: ρ udp = l T /r P r(succ Su Succ) T idle +P c T c +P s T s, (14a) ρ d tcp = l T /r P r(succ AP Succ) T idle +P c T c +P s T s nd 1 n 1, ρ u tcp = l T /r P r(succ St Succ) T idle +P c T c +P s T s nu 1 n 1. (14b) (14c) In particular, the factor n d 1 /n 1 in formula (14b) indicates the probability that when the AP is successfully transmitting a MAC frames, this frame delivers a data packets for one of the TCP downlink connections. Similarly, the factor n u 1/n 1 in formula (14c) indicates the probability that when the S t wireless station (i.e., the wireless station that models the overall TCP traffic generated by the mobile TCP senders and TCP receivers) is successfully transmitting a MAC frames, this frame delivers a data packets for one of the TCP uplink connections.

7 5 Model Validation In this section we validate the capability of our model to capture the system behavior, in particular as far as the estimation of TCP and UDP throughput performance. To this end, in this section we compare the model predictions with numerical results obtained through realistic discrete-event simulations of the system. The simulation environment we used is an extension of the one utilized in [5], with the implementation also of persistent TCP traffic flows. The TCP version we have considered is the TCP Reno [16]. As far as the p value, we used the value estimated through the iterative algorithm derived in [8] for a saturated network. Table 1 summarizes the values adopted for the physical and MAC protocol overheads during the simulations. This parameters setting is fully compliant to the mandatory setting defined in the IEEE 82.11b standard for the 11 Mbps channel rate [1]. All the results presented henceforth are obtained by executing simulation runs long enough to guaranteed a 99% confidence level with a precision lower that 1% 6. For the sake of brevity, to indicate a network with n d 1 = x, nu 1 = y and n 2 = z hereafter we will use the simplified notation T xyu z. Table 1. IEEE 82.11b configuration t SLOT τ SIF S DIF S EIF S 2 µsec 1 µsec 1 µsec 5 µsec 364 µsec P LCP hdr MAC hdr CW min CW max Data Rate 192 bits 272 bits Mbps A first set of simulation has been conducted to validate the accuracy of formulas (14b), and (14c) for evaluating the TCP throughput when no UDP traffic is present. In particular, in Figures 3, 4, and 5 we compare the measured downlink, uplink and aggregate throughput achieved by the TCP connections for different network configurations, assuming n 2 =. The lines in the graphs represent the model predictions, while the filled circles are the measured values observed during the simulations. The shown results where obtained assuming that the TCP senders transmit data packets with a payload size equal to 146 bytes. As a consequence, we used l T = 146 byets and l A = bytes to compute the analytical results. From the shown graphs, we can note that our model provides a very good match to the observed behavior in all the considered traffic configurations. The results plotted in Figures 3, 4, and 5 also indicate that the TCP flows fairly share the channel bandwidth, irrespective of the number of wireless stations that are TCP 6 The confidence interval is usually too narrow to be appreciated from the figures. Throughput (Kbps) Aggregate TCP Throughput Downlink TCP Throughput Uplink TCP Throughput Figure 3. Comparison of model predictions (lines) and observed behavior (points) for the TCP throughputs in the network scenario T n1u. receivers or senders. For instance, let us consider the results shown in Figure 3. In this case, we have a variable number n of TCP downlink flows that compete with a single TCP uplink flow, and no UDP traffic is present. We can note that when n = 1, the to flows get the same throughput, while increasing the number of downlink flows the uplink TCP throughput decreases proportionally. In Figure 4 we show the reversed situation, in which a single downlink flows compete with a variable number n of uplink TCP flows. We can observe that the system behaves in the same way, achieving both the same aggregate TCP throughout and per-flow TCP throughput. Finally, in Figure 5 we show the symmetric configuration in which the same number of uplink and downlink TCP connections contend for the network resources. The fair channel allocation is evident from the plotted results, since the curves representing the uplink and downlink TCP throughputs are practically overlapping. It is worth remarking that these results are somehow similar to what was also discovered in [15]. In particular, the authors in [15] proved that considerable TCP unfairness can occur in WLANs depending on the buffer availability B at the AP. In that paper, it was proposed to set the TCP advertised window equal to B/n such as to avoid congestion events due to buffer overflows. In this paper, we have analytically proved that setting the TCP advertised window equal to one is a sufficient condition to avoid TCP unfairness issues in hot spot networks. A second set of simulation has been conducted to validate the accuracy of formulas (14a), (14b), and (14c) in the more general cases with n 2 >. In particular, in Figures 6, 7, and 8 we compared the aggregate throughput achieved by the TCP and UDP connections for several net- x

8 6 5 Aggregate TCP Throughput Downlink TCP Throughput Uplink TCP Throughput 6 5 Aggregate TCP Throughput Downlink TCP Throughput Uplink TCP Throughput Throughput (Kbps) Throughput (Kbps) x x Figure 4. Comparison of model predictions (lines) and observed behavior (points) for the TCP throughputs in the network scenario T 1nU. Figure 5. Comparison of model predictions (lines) and observed behavior (points) for the TCP throughputs in the network scenario T nnu. 6 Conclusions work configurations and different packet payload size l. It is worth remarking that we assumed that UDP and TCP flows generate data packets with the same payload size. The lines in the graphs represent the model predictions, while the points are the measured values observed during the simulations. In particular, solid lines represent the TCP aggregate throughput computed as r (ρ d tcp +ρ u tcp), while the dashed lines represent the UDP aggregate throughput computed as r ρ udp. Since we have already demonstrated that using a TCP advertised window equal to one is sufficient to provide a fair channel allocation between downlink and uplink TCP flows, in these figures we plotted only the aggregate TCP throughput to make them clearer. From the shown graphs, we can note that our model provides a good match to the observed behavior in all the considered traffic configurations. The results plotted in Figures 6 and 7 indicate that a single UDP uplink flows can get the same throughput of all the other TCP flows, independently of their number. This is due to the fact the contention level induced by the TCP traffic is almost independent on the number of TCP flows, because the closed-loop nature of the TCP protocol auto-regulates its sending rate. As shown in Figure 8, this implies that TCP traffic is negatively affected by the presence of noncongestion-controlled traffic as the UDP traffic. In fact, the UDP traffic is inelastic, i.e., it does not adapt its sending rate to the available link bandwidth. Thus, the more are the UDP flows and the larger is the contention level in the network. This leads the TCP connections to further reduce their packet transmission rate, resulting into a significant unfairness. This paper presented a simple analytical framework to model the interaction between inelastic traffic (i.e., UDP), elastic traffic (i.e., TCP), and the IEEE MAC protocol in hot spot networks. Under the assumption of TCP advertised window equal to one, the proposed model predicts the throughput performance of downlink and uplink TCP connections contending with uplink UDP flows the channel access, in the case each source has an unlimited amount of data to send. By exploiting the developed analysis, we have shown that: i) the aggregate TCP throughput is almost independent of the number of wireless stations; ii) using a TCP advertised window equal to one ensures a fair access of the channel bandwidth to the TCP flows, irrespective of the number of downlink or uplink TCP connections, in the case no inelastic traffic is present; and iii) the presence of inelastic traffic, such as the UDP traffic, negatively affect the throughput of elastic traffic, such as the TCP traffic, inducing severe unfairness. Several fundamental aspects of the performance of TCP sessions still require investigations. Short-lived TCP connections: Today, the majority of TCP sessions in Internet deliver a quite limited amount of data (e.g., the web pages carried over HTTP traffic). For short-lived TCP flows a relevant performance index is not only the throughput achieved, but also the mean delay required to complete the session. Our model could be extended to take into account a realistic distribution of the TCP session durations, for instance following the modeling approach proposed in [11].

9 Throughput (Kbps) TCP - l=536b UDP - l=536b TCP - l=124b UDP - l=124b TCP - l=146b UDP - l=146b Throughput (Kbps) TCP - l=536b UDP - l=536b TCP - l=124b UDP - l=124b TCP - l=146b UDP - l=146b Figure 6. Comparison of model predictions (lines) and observed behavior (points) for the network scenario T nu1. n Figure 7. Comparison of model predictions (lines) and observed behavior (points) for the network scenario T nnu 1. n TCP flows with different RTTs: In our analysis, as well as in the simulations, the TCP flows, either originate or terminate at the AP, such as to have the same RTT. However, in general the TCP flows originate and terminate in the wired part of the network, following different paths and experiencing different RTTs, which could significantly affect the TCP sending rate. Our model could be extended to take into account different RTTs. Non-asymptotic UDP flows: Inelastic traffic is unresponsive traffic, which does not adapt its sending rate to the available link bandwidth. Considering asymptotic UDP traffic implies that the UDP sources operate in saturated condition. However, several applications generate UDP traffic according to specific traffic patterns (i.e., Constant bit Rate, On-Off, etc.), resulting into non-saturated UDP sources. Our model could be extended to take into account the presence of nonasymptotic UDP flows. References [1] Part 11: Wireless LAN medium access control (MAC) and physical layer (PHY) specification/amendment 2: Higherspeed physical layer (phy) in the 2.4 ghz band, November 21. [2] A. Balachandran, G. Voelker, and P. Bahl. Wireless Hotspots: Current Challenges and Future Directions. In Proceedings of 1st ACM Workshop on Wireless mobile applications and services on WLAN hotspots (WMASH 3), pages 1 9, San Diego, CA, September [3] G. Bianchi. Performance Analysis of the IEEE Distributed Coordination Function. IEEE J. Select. Areas Commun., 18(9): , 2. [4] L. Bononi, M. Conti, and E. Gregori. Runtime Optimization of IEEE Wireless LAN Performance. IEEE Trans. Parallel Distrib. Syst., 15(1):66 8, January 24. [5] R. Bruno, M. Conti, and E. Gregori. Optimization of Efficiency and Energy Consumption in p-persistent CSMA- Based Wireless LANs. IEEE Trans. Mob. Comp., 1(1):1 31, mar 22. [6] R. Bruno, M. Conti, and E. Gregori. Modeling TCP Throughput over Wireless LANs. In Proceedings of IMACS25, pages , Paris, France, July [7] R. Bruno, M. Conti, and E. Gregori. Stochastic Models of TCP Flows over WLANs. Technical Report 11, IIT - CNR, April 25. [8] F. Calí, M. Conti, and E. Gregori. Dynamic Tuning of the IEEE Protocol to Achieve a Theorethical Throughput Limit. IEEE/ACM Trans. Networking, 8(6): , 2. [9] A. Chandra, V. Gummalla, and J. Limb. Wireless Medium Access Control Protocols. IEEE Communications Surveys, 2:2 15, 2. [1] R. G. Gallager. A Perspective on Multiaccess Channels. IEEE Trans. Inform. Theory, 31(2): , [11] A. Kherani. and K. Kumar. On Processor Sharing as a Model for TCP Controlled HTTP-like Transfers. In Proceedings of ICC 24, Paris, FR, 24. [12] L. Kleinrock and F. Tobagi. Packet Switching in Radio Channels: Part I - Carrier Sense Multiple-Access Modes and their Throughput-Delay Characteristics. IEEE Trans. Commun., 23: , [13] D. Miorandi, A. Kherani, and E. Altman. A Queueing Model for HTTP Traffic over IEEE WLANs. In Proceedings of 16th ITC Specialist Seminar on Performance Evalu-

10 Throughput (Kbps) TCP - l=536b UDP - l=536b TCP - l=124b UDP - l=124b TCP - l=146b UDP - l=146b n Figure 8. Comparison of model predictions (lines) and observed behavior (points) for the network scenario T nnu n. ation of Mobile and Wireless Networks, Antwerp, Belgium, September [14] J. Padhye, V. Firoiu, D. Towsley, and J. Kurose. Modeling TCP Throughput: a Simple Model and its Empirical Validation. IEEE/ACM Trans. Networking, 8(2): , April 2. [15] S. Pilosof, R. Ramjee, D. Raz, Y. Shavitt, and P. Sinha. Understanding TCP fairness over Wireless LAN. In Proceedings of IEEE Infocom 23, volume 2, pages , San Francisco, CA, March 3 April [16] W. Stevens. TCP Illustrated, Volume 1: The Protocols. Addison-Wesley, New York, NY, July 21. [17] Y. Tay and K. Chua. A Capacity Analysis for the IEEE MAC Protocol. Wireless Networks, 7: , 21.