Stability Analysis of Active Queue Management Algorithms in Input and Output Queued Switches in Heterogeneous Networks

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1 Stability Analysis of Active Queue Management Algorithms in Input and Output Queued Switches in Heterogeneous Networks Rahim Rahmani Oliver Popov Mid Sweden University SE Sundsvall, SWEDEN Abstract: The focus of the paper is the implementation of a class of active queue management algorithms (AQM). Their measure of congestion includes packet arrival rate such as REM and Adaptive AQM (AAQM) with respect to a combined input and output queued (CIOQ) switch. The selection of parameters for the congestion controllers at the sources and the AQM scheme at the links prove to be essential for ensuring stability. A structure with one AQM per output port is proposed and consequently followed by the analysis of the constraints on the switch fabric speed imposed by it. A three queue model of a CIOQ switch is developed and simulated to validate the design and compare its performance with a RED queue switch. Keywords: Active Queue Management (AQM), Input and Output Queued Switches (IOQS), heterogeneous networks, congestion management. 1. Introduction The result of the world-wide proliferation of the Internet, the combinatorial growth of users, the infusion of heterogenity in the infastructre (wireline and wireless), the diversity of bandwidth hungry multi-media and peer-topeer applications, is a congested network that induces serious packet losses and delays. Consequently, there has been a surge of interest in designing best-effort service networks that can deliver low-loss, low-delay and adequate utilization of capacity. An extensive research has been performed on analysis and design of various active queue management(aqm) algorithms. The controller structure, stability and speed have been studied analytically and empirically [1],[2], and [10]. Several AQM schemes have been proposed in recent literature to provide early congestion notification to users. The main motivation behind this area of research is to provide a low-loss, low-delay service over the current Internet. Some of the recently proposed AQM schemes include the RED [1], REM [4] algorithms detect congestion based on the queue length at the link, the AAQM algorithm detect congestion based on the arrival rate into the link. The new algorithms have so far been studied only in the context of a single queue link with a well-defined service capacity. Devices such as combined input and output queued (CIOQ) switches [9] have multiple queue whose capacities depend on the cross traffic between multiple input and output interfaces. This paper proposes a simple rule to design the speed of adaptation at the link that ensures the stability of the system and give a structure for implementing these new arrival rate based AAQM in a CIOQ. 1.1 AAQM Background We adopt the system model introduced in [13]. Namely, consider a network with a set L of links and let C l and γ l be the capacity and the desired utilization. We refer to the ratio of the maximum arrival rate (that can be supported by the link to guarantee a desired small loss probability) to the link capacity. Let a switch S be a non-empty set of links and S be the set of all switches in the Network. We will associate a flow with each switch. Let flow S generate traffic at rate X s. The rate X c is assumed to have a utility c log (X c ) to user C. Following the notation of [14],[15] for each flow C, let d 1 (c,j) be the delay from the source of switch C to the link j and d 2 (c,j) be the feedback delay from the link j back to the source. Let T c be the total round-trip delay for switch C. Note that for all j L such that switch C traverses link j we have T c = d 1 (c, j) + d 2 (c, j). Let each link L in the network generate feedback in the form of Explicit Congestion Notification (ECN) [3] Marks.

2 Assume that the fraction of packets marked is a function of the total arrival rate (λ l) and a parameter B l. This means the cumulative sum of the packets of all of the aggregates using a link is less than the bandwidth of the link. The total marks are distributed among the users in proportion to their flow rates. Let P l (λ l + B l ) be the fraction of total flow that is marked by link l. The marking function at each link l L, P l(q + s ), q 0, s 0 is assumed to be strictly increasing in q and strictly decreasing in s and continually differentiable in both its arguments. Now let each user C employ the weighted Proportionally fair congestion-control algorithm [13]. χ c=k c c χ( c t Tc ) pl ( χj ( t d1 ( j, l) d2( c, l), Bl ( t d2( c, l))) l: l C j: l j c S,n (1) Figure 1.CIOQ Switch The switching fabric is the center element of the switch. It can be classified into different division form of time or space and the former are characterized by a common communication channel resource shared by all input and output ports [9]. Where k c determine the speed of the congestion-control and c is the weight or the willingness to pay of user C. The AAQM can be ~ C l = α ( γlcl χ j( t d1( j, l))) j : l J l L (2) Where α is the control gain, which determines the speed of adaptation. C l is capacity and γ l is the desired utilization. 1.2 Switch Background To simplify the design and implementation of scheduling algorithms switches usually operate with a speed-up. In this case buffering is required at outputs as well as inputs due to the difference in speed between the internal memories and the links. They are termed as combined input/output queuing (CIOQ) and the conceptual structure is shown in Figure 1. A switch consists of the three major components the input interfaces, the output interfaces and the switching fabric. The input/output may have a number of physical interfaces. Figure 2. CIOQ Switch Module One of the methods to reduce HOL (Head Of Link) blocking is to increase the speedup of a switch [9]. A switch with the speedup of S can remove up to S packets from each input and deliver up to S packets to each output within a time slot, where a time slot is the time between packet arrivals at input ports. An example of CIOQ module is shown in Figure 2. The nine separate input queues for each of the three input interfaces allow the switch to have nine different output interfaces.

3 The module has three output interfaces and therefore has three output queues. This paper is organized as follows. In section 2 we describe the proposed AAQM architecture. The technology of AQM constraints in the switch fabric is studied in section 3. In section 4 we describe the simulation model of AQM switch. In section 5 we explain the effect of speed up for RED, REM and AAQM and section 7 concludes the paper. 2. Proposed AAQM Architecture W.l.o.g., in the analysis the queuing architecture of the switch fabric is abstracted from the physical implementation. The parameters that are used to define the switch fabric are as the set of input ports, denoted by I, and the set of output ports denoted by O. Let N Q be the total number of queues N Q = N (2 N -1), we define X i as the aggregate traffic arriving at input interface i, i = 1,.. The traffic arriving at input interface i destined for output interface j is X ij. Arrivals at each switch inputs are a stochastic process A, which is a sequence of arrival packet. Each input module has a schedule S for example Weighted Fair Queue (WFQ), which determine the next packet to forward to the switch fabric input port. Figure 3 illustrates an example of the proposed architecture of AAQM switch. The queue length evolution for each input interface described by the : X i+1 =X i +A i D i, i 0 and D is the departure of the packet. Let C I i be a set of input interfaces. Each input interface i is a set of an element in the set C I i and has capacity Ci, q. The C I i is an binary row vector of size N (2 N -1) i.e. C I I I i = [ Ci, q,..., Ci, q ] with NQ C I i, q =1 iff queue q in input module store X i from input interface i, i= 0,., N-1. Each output module has a set of output interfaces. Each output interface j is an element in the set O. Similarly to the definition for input interface capacity let C O O O j = [ C j, q,..., C j, q ] with NQ Ci, O q =1 iff q output j, j= 0,., N-1 is the traffic arriving Figure 3. AAQM Switch Architecture at the input of the output module from switch fabric output port. To measure the total packet arrival rate X ij and packet backlog B ij destined for output interface j as well as the output interface capacity C IO i, j must be measured. The capacity C IO i, j can be estimated by Ci, IO j = C I i Λ C O j, where Λ denotes logical and, the element of the binary vector C IO i, j corresponding to queue (q) is 1 iff q stores packet from input i destined to j. The maximum rate at which these B ij and X ij measurements need to be communicated from the input module to the AQM algorithm is at each packet arrival. The total packet arrival rate X j and backlog B j is calculated as input into the AQM algorithm as:

4 I X j = χ (3) i= 1 I ij B j = + Bij B Aj i= 1 (4) Where B Aj is the packet backlog in the output interface j. Now that each of input of the AQM has been described the AQM (1) can be evaluated to update the marking / dropping rate P l. The marking and dropping strategy is different. For ECN capable packets the mark-front and markrelay strategies investigated in [8] [21] reduces the feedback time of the congestion signal. Therefore ECN capable packets are randomly marked packet in the output module [5]. Non- ECN capable packets are randomly dropped. The dropping of the packet should be done before packet forwarding through the switch fabric and avoids wasting switch fabric and buffer capacity. 3. The technology of AQM constraints in the switch fabric Let us assume that (1) the end-to-end flow control is stable, and (2) source rates converge to a steady state at or below the network capacity. It is easy to show that as long as output interface capacity is the only bottleneck (this is especially true for heterogeneous networks because of the wireless part) in steady state, a single AQM per output port design is sufficient. The criteria to achieve this are: 1. Stable matching of input ports to output ports by scheduler [18],[19]. 2. The switch fabric input interfaces capacity should be able to transfer all of the incoming traffic from input module: Cin mod C I i, q,i= 0,., N-1 (5) 3. The switch fabric output interfaces capacity should have enough buffer capacity for fully load of all of the output interfaces of the output module: Cout mod Ci, IO j, i=0,.,n-1,and j=0,.,n-1 (6) 4. AQM Simulation In order to compare the RED, REM and AAQM, we performed a set of simulation with the ns simulator[6]. Our simulation model shown in Figure 4 in scenario with TCP traffic. The scenario describes the simulation of different node movements, which are common in a heterogeneous network. Figure 4. Model of AQM switch The switch fabric speedup is S. The switch has nine input interfaces. Each source S1 to S9 is capable of hosting an arbitrary of TCP sessions. During each simulation the network was given a warm up time of 10 seconds to avoid any stranger behavior caused by the large number of TCP sessions for each of the experiments using both the TCP/Reno and TCP/Vegas transport protocol versions. The buffer sizes (the input and output queue sizes ) was increased in fix steps between 10 and 100 packets. The AQM used in the switch is the AAQM. From (2) by using α as the control gain and that determines the speed of adaptation. C l as capacity and γ l is desired utilization. All sources were ECN enabled except drop-tail. The buffer size vary between 10, 20, 35 50, 75 and 100 packets. Each AQM with the specific buffer size is used in the scenario and simulated several times to get a good and reliable value.

5 Port Input Output Bandwid & RTT 10Mb, 20ms 2 MB 25ms Queue sizes 10,20,35,50, 75,100 10,20,35,50, 75,100 Table 1. Simulation Parameters 5. The Effect of the Speedup TCP session Speedup sometimes also referred to as switching capacity is a measure of the relative speed of the switching fabric as compared to that of the input (or output ) links. Speed up is provide to clear output contention faster or to reduce effects of internal blocking. For each speedup the mean backlog was taken over a 510 seconds simulation of which the results are kbit/s Throughput Queue size Figure 5. Evolution of the Throughput based on the last 500 seconds. The first 10 seconds is a warm up period. During the simulation period 25 TCP session were started and stopped with the uniform random start times over the simulation period. The rate based AQM switch has lower mean total backlog than the drop-tail switch. The drop-tail, RED and some times REM switches maintains full buffers because it is unable to signal congestion until the buffer overflows. The speed up of the output buffers should be larger than the input buffer and that any services differentiation for scheduling of packets needs only to be performed at the output queue, since where all most queuing delay occurs. RED REM AAQM % Loss Queue size Figure 6. Evolution of the Loss. RED REM AAQM The AAQM works really well on small queue sizes. In fact it has a slightly less throughput as the other two algorithms, which is shown in Figure 5. The dropped packets are due to the queue overflow. It is clear that REM and RED do not mark enough packets to signal to the TCP sources to slow down in time. That is why in their case there is a higher loss, especially at small queue sizes which is shown in figure 6. AAQM is more aggressive in marking packets and manage to lower the transmission rate of the sources quickly. REM suffers surprisingly from high loss on the TCP flows despite a small target queue size that should mark packets in an early stage. 6. Conclusions The article discusses and presents architecture for implementing AQM in the CIOQ type of switches. The results indicate that the length of queue should be under control to some small values in order to avoid bias against bursty traffic and long queuing delay. This is also consistent with the concerns related to QoS, since queues controlled to small values produce small jitter and predictive delay guarantees for end users. It will be of interest to explore the architecture of the switch fabric with respect to other queue management algorithms and under varying conditions on the network.

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