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A high-performance ATM switch based on modified shuffle-exchange network
Computer Communications 22 (1999) 110–119
A high-performance ATM switch based on modified shuffle-exchange network Hasan C ¸ am* Computer Engineering Department, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia Received 22 October 1997; received in revised form 11 September 1998; accepted 24 September 1998
Abstract This paper presents an output buffering ATM switch, called modified shuffle-exchange network (MSN) that is obtained by inserting a connection pattern just after every other shuffle-exchange stage. The purpose of modifying a shuffle-exchange network by inserting a connection pattern is to reduce significantly the number of its internal conflicts. Each link of every other stage of MSN has a filter to route successful packets to their destinations. Instead of employing the traditional destination tag routing scheme on MSN, we developed a fast destination tag routing scheme, called FDR, for MSN. In the traditional destination tag routing scheme, the routing tag of a packet is made equal to its destination address. In FDR, however, the routing tag of a packet is determined by its destination address as well as source address. FDR often requires less than log2 N stages to route a packet from its source to destination, which leads the traffic load to be reduced at the successive stages of the network. An analytical model is presented to analyze the performance of MSN under uniform traffic. Under a variety of traffic models, including uniform, hot-spot, ATM bursty, and output concentration, extensive simulations are run to examine and compare the performance of MSN with two existing similar networks. The simulation results show that MSN with FDR improves the packet loss probability substantially. 䉷 1999 Elsevier Science B.V. All rights reserved. Keywords: Shuffle-exchange network; Internal conflict; Destination tag routing scheme; Output buffering ATM switch; Performance evaluation
1. Introduction Fast packet switching technique such as asynchronous transfer mode (ATM) is considered to be the most appropriate switching technique for the transmission of voice, data, images and video in an integrated fashion. The challenge is to design and build packet switching networks capable of switching relatively small packets at extremely high rates [4]. Multistage interconnection networks (MINs) such as banyan networks are listed among the most desirable building blocks for fast packet switching networks. Among the main advantages of a banyan network are selfrouting, low hardware complexity compared to crossbar switch, distributed control, suitable for VLSI implementation, modular and scalable [1–3]. The main disadvantage of banyan networks is to have a limited number of connection patterns, which results in a significant number of internal conflicts in switching elements (SEs). To make banyan networks suitable for ATM switches, this paper presents a modified shuffle-exchange network (MSN) that has a much * Tel.: ⫹ 966-3860-2147; fax: ⫹ 966-03860-3059; e-mail: cam@ ccse.kfupm.edu.sa
smaller number of internal conflicts than a shuffle-exchange network. As MSN is an output buffering ATM switch with packet filters at the links of stages, a new self-routing algorithm, called fast destination tag routing scheme (FDR), is introduced to improve the performance. As the incoming traffic to a banyan network is usually not known in advance, multiple packets arriving simultaneously at different input ports may have to be forwarded along the same internal link. This leads to the main drawback of banyan networks, called internal conflict: two packets destined for different outputs of the network request simultaneously the same output link of a given SE. Another important problem that any MIN has to deal with is the output contention in which multiple packets are destined to the same output port. Both internal conflict and output connection severely degrade the throughput performance and the packet loss probability of a banyan network. To reduce the adverse effects of the internal conflict and output contention, one solution is to add extra stages to banyan network and provide output buffering, as in the tandem banyan switching fabric (TBSF) [4] and MS4 [5]. TBSF consists of K banyan networks in series. MS4 is constructed using K ⱖ n log2 N shuffle-
0140-3664/99/$ - see front matter 䉷 1999 Elsevier Science B.V. All rights reserved. PII: S014 0-3 664(98)00257 -6
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Fig. 1. A 7-stage MSN with 16 inputs/outputs. The odd-numbered and even-numbered stages of MSN are identical to the shuffle-exchange and a -exchange stages, respectively.
exchange stages, each with N/2 unbuffered SEs and N inputs/outputs. Outputs of stages n to K are also connected to the inputs of the same-number output port modules (OPMs) through filters. MS4 is motivated by the observation that those misrouted packets that are marked invalid in TBSF waste the switching resources because they are not allowed to re-start routing until the next banyan network. Therefore, similar to an earlier proposed ATM switch called rerouting network [6], MS4 starts rerouting a misrouted packet just after it loses contention. To achieve rerouting in MS4, each packet has a counter field (C) of dlog2 ne bits that is initially set to n. Whenever a packet successfully passes through a stage of MS4, its counter C is decremented by 1, and each time a packet loses contention its counter is reset to n. The proposed network MSN in this paper also starts immediately re-routing a misrouted packet, but FDR can set its counter to a number smaller than n depending on the minimum distance between the packet and its destination. This directly translates into higher throughput in MSN, since packets remain for little time within the network on average and therefore consume less network resources [7]. Also, filters in MSN are located at the output links of every other stage, which leads to a reduction in the hardware complexity. The traditional destination tag routing scheme is a selfrouting distributed-control procedure used to establish a path from any input port of banyan network to any output port. Specifically, to route a packet destined to an output port of banyan network, say d, with binary representation d1d2…dn (where d1 is the most significant bit), the destination routing scheme uses the destination address d1d2…dn as the routing tag for the packet. In the proposed FDR, the routing tag of a packet is determined by both its destination
address and source address, which usually leads the routing tag to have less than n bits. The rest of the paper is organized as follows. In Section 2, we introduce MSN and FDR. Section 3 presents an analytical model for MSN under uniform traffic, and compares the performance of MSN, MS4 and TBSF using simulation results under uniform and nonuniform traffic patterns. Concluding remarks are made in Section 4.
2. Architecture of MSN MSN is designed with the following goals in mind: 1. Reduce the number of internal conflicts that occur in the SEs of a shuffle-exchange network. 2. Whenever it is not possible to avoid having internal conflicts among four packets arriving at two SEs of a stage, route correctly those packets that are closest to their destinations. 3. Whenever a packet is misrouted (or deflected) to a wrong outlet of an SE as a result of conflict, first compute its new routing tag based on the minimum distance between the packet and its destination and, then, start immediately re-routing the packet. To achieve the first part of goal 3, we developed FDR to compute a new routing tag based on the minimum distance. To start rerouting immediately and easily, the stages of a network should be identical and, therefore, we have chosen shuffle-exchange network to realize the second part of goal 3. To accomplish goals 1 and 2, we introduce an a exchange stage that is inserted just after every other shuffle-exchange stage. These three goals together aim to
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Fig. 2. (a) Those control bits that would have conflicts on two SEs of a banyan network can be routed successfully through the SEs of a core network in MSN. (b) Any set of control bits that do not have conflicts on two SEs of a banyan network are also routed successfully through the SEs of a core network in MSN.
improve the network performance by preventing especially those packets that are very close to their destinations from being misrouted in case of a conflict, thereby increasing the number of successful packets and reducing the possibility of occurring conflicts in SEs of the successive stages. Let a denote a connection pattern such that, for 0 ⱕ i ⱕ N ⫺ 1; input i of the pattern is connected to output i or
Fig. 3. Algorithm SET-SE used for setting each switching element of MSN.
i ⫹ (N/2) mod N based on that i is even or odd, respectively. a -exchange is defined as being a stage consisting of the connection pattern a followed by a column of N/2 bitcontrolled SEs of size (2 × 2) each. As shown in Fig. 1, MSN is constructed by inserting an a -exchange stage just after every other shuffle-exchange stage, where each stage has N/2 unbuffered binary SEs. MSN stages are labeled from left to right starting with 1 up to K. The odd-numbered and even-numbered stages of MSN are identical to the shuffle-exchange and a -exchange stages, respectively. Any SE of an even-numbered (respectively, odd-numbered) stage is called even-SE (respectively, odd-SE). The outlets of every odd-SE are connected to the inputs of the same number OPMs through filters. As in TBSF and MS4, OPMs perform buffering and concentration functions. The SEs of each stage in MSN are labeled from top to bottom, starting with 0 until 2 n⫺1 ⫺ 1. For 0 ⱕ j ⱕ 2n⫺2 ⫺ 1, the jth and j ⫹ 2n⫺2 th SEs of each stage form a pair j. Thus, each stage has 2 n⫺2 pairs of SEs. Note that the four outlets of pair j of odd-SEs are connected to the inlets of pair j of even-SEs through the connection pattern a . These two pairs of odd-SEs and even-SEs are said to form a core-network with 4 inputs/outputs, as shown in Fig. 2. The odd-SEs of a core-network act somewhat like sorting cells introduced in [9] in the sense that their main function is to prevent even-SEs from having some conflicts. Therefore, the number of internal conflicts in MSN depends on how much a core-network is successful in preventing internal conflicts on its even-SEs. Let a and b (respectively, c and d) be the control bits of an odd-SE (respectively, the other odd-SE) of a core-network, where control bit refers to a destination address bit used in setting SE. If {a, b} {0,1} and {c,d} {0,1}, no conflict occurs in the even-SEs of the core-network similar to SEs of any banyan network, as shown in Fig. 2(b). But, if {a,b} {0,0} and {c,d} {1,1}, no conflict occurs in the even-SEs either, as shown in Fig. 2(a). Also note that some active packets arriving at inputs of a core-network may not reach any outlet of an even-SE of the network because filters at the outlets of odd-SEs may route them to OPMs because their counters are zero, which helps reduce the possibility of having internal conflict in even-SEs. Algorithm SET-SE, shown in Fig. 3, describes how to set both an even-SE and odd-SE, and shows when a filter extracts successful packets to their destinations. Each packet header in MSN comprises an activity bit a, its binary destination address d1 d2…dn, a counter field C of [log2 n] bits, and a conflict bit w. The activity bit a indicates whether an input receives a packet (a 1) or does not receive (a 0). Whether an SE will be set to cross or straight depends upon the activity bits (a u, a l), the counters (C u, C l), and the control u l u ⫹1 and d bits dn⫺C n⫺C l ⫹1 of the packets arriving at the inputs of the SE, where superscripts u and l stand for upper and lower, respectively, to distinguish the packets of the upper and lower inputs of an SE. In case of an internal conflict, the
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Fig. 4. The state transition diagram of a packet.
packet with smaller counter value is routed correctly because it is closer to the destination. If no packet arrives at the inputs of an SE of MSN, then no action is taken and the SE is left in its present state (line 1 of SET-SE). If one of the inputs of an SE does not receive a packet, the SE is set according to the control bit of the available packet (lines 2 to 3). If both inputs receive a packet and the control bits form the set {0,1}, then the SE does not have a conflict and is set accordingly (line 4.1). If SE has a conflict because the control bits of the packets are the same, then the packet with smaller counter value is routed correctly (lines 4.2 and 4.3); if the counter values are the same, then the packet to be routed correctly is selected randomly (line 4.4). Initially, all conflict (i.e., w) bits are reset to zero. Whenever a packet loses contention, its conflict bit is set to 1 (line 4.6). If the counter of a packet that is routed correctly in an odd-SE is less than or equal to 1, then the packet is distinguished and routed to its destination by a filter (line 6.2.1). If a packet reaches an outlet of an even-SE with a conflict bit of 0 (respectively, 1), then its counter is decremented (respectively, initialized by FDR), as shown in lines 6.1.1 and 6.1.2 of SET-SE. 2.1. FDR The destination tag routing scheme works in omega network as follows [8]. Assume that the stages of omega network are labeled in ascending order from left to right, starting with 1, and the outputs of each stage are labeled in m m ascending order from 0 to N ⫺ 1. Let im im 1 i2 …in and r r r r d d1 d2 …dn denote the input m and the output r, respectively,of omega network, where 0 ⱕ m, r ⱕ N ⫺ 1. Now, let us suppose that a packet, say A, arriving at input port i m is destined to the output port d r. The destination tag routing scheme initializes the routing tag of packet A to d r. If packet A does not encounter any internal conflict, stage k switches m m r r packet A from its input im k ik⫹1 …in d1 …dk⫺1 into the output m m m r r ik ik⫹1 …in d1 …dk for k, 1 ⱕ k ⱕ n. Thus, stage n finally switches packet A into the output port d r. The basic idea behind FDR is to eliminate the need for routing packet A through the first k stages if the following m m r r r and already holds: im n⫺k⫹1 in⫺k⫹2 …in d1 d2 …dk m m m r r r r in⫺k in⫺k⫹1 …in 苷 d1 d2 …dk dk⫹1 . After determining k, FDR r r dk⫹2 …dnr and initializes the routing tag of packet A to dk⫹1 sets the counter field C of packet A to n ⫺ k. As an example
for N 16, if a packet with destination address 1100 arrives at input port with address 0110, the value of k for the packet will be 3 because the last three bits i2i3i4 ( 110) of the input port address are the same as the first three bits d1d2d3 ( 110) of the destination address. So, the packet needs to be routed correctly through one stage only according to d4 0 and, therefore, the counter field C of the packet is initialized to 1. 2.2. Packet sequencing Assume that the last stage, stage K, of MSN is an old numbered stage. Let t s denote the maximum delay incurred at a SE of MSN, and T denote the packet duration in bit times. For an ATM packet, T equals 424 because any ATM packet has 424 bits. Assume that packets A and B are destined to the same output port, and packet B arrives in the same input port of MSN just after packet A. The worst case happens when packets A and B are successfully routed to OPMs by the filters of stages K and 1, respectively. This implies that packets A and B are considered successful after K.t s and T ⫹ t s bit times. If each OPM is assumed to be a FIFO queue such that the location of a packet is determined by the arrival time of its first bit, then the condition for preserving the order of packets A and B in the worst case is K.t s ⬍ T ⫹ t s or ((K ⫺ 1) t s / T) ⬍ 1. To satisfy this condition for large K, additional artificial delays can be inserted into those inputs of each OPM that are connected to the leftmost stages of MSN. 3. Performance of MSN The performance of MSN has been evaluated under different traffic models. A traffic model is determined by the destination request distribution of arriving packets, and the process describing the arrival of packets at the input ports of the network. The simplest traffic model is the uniform traffic in which the process describing the arrival of packets at the input ports is an independent and identically distributed Bernoulli process with the load parameter p (0 ⬍ p ⱕ 1). We assume that a packet arrives at a given input port in a given timeslot with probability p. As for the destination request distribution of arriving packets under uniform traffic, each packet chooses its destination port uniformly among all output ports, independently from all
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previous and current arriving packets. In evaluating the performance of a self-routing ATM switch, packet loss rate Ploss is usually more important than delay. Ploss, being the fraction of packets lost within the switch, is required to be lower than 10 ⫺6 in most ATM switches. In the comparison of switches, we assume that no packet is lost in any OPM. 3.1. Analysis of MSN In this section, the performance of MSN is analyzed under uniform traffic. We assume that packets arrive at the inlets of any (2 × 2) SE independently of each other, and a packet chooses a particular outlet of an SE with probability 1/2. A packet of MSN has n ⫹ 1 states labeled from 0 to n, where state i, 0 ⱕ i ⱕ n, represents that packet’s counter C equals i. The state transition diagram of a packet is shown in Fig. 4. In this diagram, the event of not having a packet at an input port with probability 1 ⫺ p is also represented by state 0. When a packet arrives at an input port or loses contention in an even-SE, FDR initializes its counter C to one of the numbers ranging 1 to n. As described in algorithm SET-SE, a packet with state i moves to state i ⫺ 1 with probability Wi in an even-SE. Thus, Wi is the probability that a packet wins in state i. Li refers to the ‘‘loss’’ probability of a packet in state i so that Li 1 ⫺ Wi. When a packet in state i loses contention, the probability that FDR initializes its counter to one of the states i, i ⫹ 1,…, n is Li/(n ⫺ i ⫹ 1). Let Qi(k) denote the probability that a link at stage k of MSN carries a packet with state i, for 1 ⱕ k ⱕ K, where K is the label of the last stage. This implies that Q0(k) represents all those packets that successfully reach their destinations prior to stage k. As the arrival process of any packet at MSN is assumed to be independent and identically distributed Bernoulli process with parameter p, the probability that an input port does not receive any packet is 1 ⫺ p, that is, Q0(1) 1 ⫺ p. To determine Qi(1) for the other i’s as well, let a denote the summation of all integers from 1 to n inclusive. As the counter C of a packet with destination address d1d2…dn is set to n ⫺ i at an input port address x1 x2 …xn by FDR if x1⫺i⫹1 …xn d1…di and xn⫺i xn⫺i⫹1…xn ^ d1…didi⫹1, we assume that Qi(1) ip=a. Let Qi(K ⫹ 1) denote the probability that an outlet of an SE at the last stage K carries a packet with state i. As any packet in a state other than state 0 that reaches an outlet of an SE at the last stage is lost, the throughput of MSN equals Qi(K ⫹ 1). The normalized throughput is given by Q0(K ⫹ 1)/p. Thus, the mean Ploss is equal to 1 ⫺ [Q0(K ⫹ 1)/p]. Let us consider a core-network shown in Fig. 2 where the even-SEs belong to an even-numbered stage r between 2 and K. The upper and lower inputs of an even-SE of the core-network are assumed to be labeled arbitrarily by X and Y. A packet, denoted A, with state i arriving at input X loses contention to a packet B arriving at input Y if and only if: packet B also requests the same outlet (this occurs with
probability 1/2) and either packet B has C i and is chosen to be winner by function random (u,l) (this occurs with probability Qi(r)/2) or packet B is closer to itsPdestination with 1 ⱕ C ⬍ i (this occurs with probability i⫺1 j1 Qj r). But, input Y is connected to an outlet of an odd-SE of the core-network and packet B is one of those two packets that arrived earlier at the inputs of the odd-SE. This implies that the probability that packet B requests the outlet of the oddSE connected to Y is 1/2. Consequently, each probability of conditions 1 and 2 is multiplied by 1/2. Thus, the loss probability Li(r) that packet A with state i loses contention to packet B is given by 2 3 ⫺1 141 1 i ⫺ 1 iX Q r ⫹ Qj r5 Li r 4 4 i 2 i j1 As Wi(r) 1 ⫺ Li(r), the probability Wi(r) that a packet with C i wins contention in an even-SE of stage r is computed by: ⫺1 1 i ⫺ 1 1 iX Q r ⫺ Q r Wi r 1 ⫺ 16 i i 8 j1 j We obtain from Fig. 4: Q0 r ⫹ 2 Q0 r ⫹ Q1 r·W1 r Qi r ⫹ 2 Qi⫹1 r·Wi⫹1 r ⫹
i X j1
1 ⫺ Wj r; Qn r ⫹ 2
n X j1
1 Q r n⫺j⫹1 j
1 ⱕ i ⱕ n ⫺ 1
1 Q r:1 ⫺ Wj r n⫺j⫹1 j
By solving these recursive equations for even integers r 2, 4, 6,…,K ⫺ 1, the mean Ploss which equals 1 ⫺ [Q0(K ⫹ 1)/p] can be computed for different values of n and K. 3.2. Simulation results Extensive computer simulations are run under different traffic patterns to evaluate and compare the performance of MSN, MS4 and TBSF. In all simulation results, any point has been obtained by averaging over ten independent simulation runs. A 90% confidence interval on the order of 10 ⫺7 was observed for packet loss rates in the 10 ⫺6 range. As packet losses that occur at OPMs are a function of the output buffer sizes and the main sources of packet losses are internal conflicts rather than output port contentions [4,5], the simulation results for the packet loss rate of MSN, MS4 and TBSF do not include those packet losses occurring at OPMs. 3.2.1. Uniform traffic In the simulations, the destination of each arriving packet at an input port is set randomly by a random number generator to simulate the destination request distribution function
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Fig. 5. The packet loss rates of analytical and simulation models versus the number of stages for different values of N at full load of MSN.
under uniform traffic. We first validate the analytical model of MSN against the results obtained by computer simulations. Fig. 5 shows the packet loss rate of analytical and simulation models as a function of K (the number of stages) at full load (p 1) for N 128 and N 1024, where the analytic results match closely with simulation results. Next, we compare the performance of MSN, MS4 and TBSF using simulation results. Figs. 6 and 7 compare the packet loss rates of MSN, MS4, and TBSF as a function of K for N 1024, at full load and half load, respectively. The number of stages required to achieve a low packet loss rate in MSN is lower than the number of stages required in MS4 and TBSF. This is an expected result because MSN reduces internal conflicts, compares the counter of a packet with
three other counters rather than just one counter in case that there is a conflict in a core-network, and employs FDR to minimize the number of stages that a packet should be routed through. 3.2.2. Nonuniform traffic 1. Hot-Spot Traffic (HST): When a large number of packets arriving at input ports are destined to the same output port, internal conflicts rapidly increase on the paths heading towards the destination and, therefore, the output port is called hot spot. The traffic directed at the hot spot is sometimes called hot traffic, and the remaining traffic is called cold traffic. HST occurs in many systems and reallife applications. For instance, in case of multiprocessors,
Fig. 6. Comparison of the packet loss rates of MSN, MS4 and TBSF under uniform traffic and full load for N 1024.
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Fig. 7. Comparison of the packet loss rates of MSN, MS4 and TBSF under uniform traffic and p 0.5 for N 1024.
many multiprocessors may request to access the same memory module. Let h represent the fraction of packets destined to the hot spot. We assume that hot spot and the destinations of cold traffic packets are chosen uniformly among all output ports. For N 128, Fig. 8 shows the packet loss rates of MSN, MS4, and TBSF versus the number of stages for h 0.5 at full load under HST. As h 0.5, N/2 packets are destined to a single output port and, therefore, packet loss rates are very high in the switches. 2. Output-Concentration Traffic (OCT): In this model, all arriving packets at input ports are destined to only a subset of all output ports. Assuming that the subset contains L output ports, the destination of a packet is
chosen uniformly among all L members of the subset. Two extreme cases of this model, namely maximum- and minimum-distance OCT (MAXDT and MINDT, respectively), are considered in [4, 5]. In MAXDT, the subset contains all N/2 odd-numbered (or even-numbered) output ports. In MINDT, the subset contains N/2 consecutive output ports (e.g., the upper half of the output ports). Figs. 9 and 10 compare the packet loss rates of MSN, MS4, and TBSF for N 1024 at full load under MAXDT and MINDT, respectively. 3. Bursty Traffic (BT): To capture the correlation in the time domain among packets originating from the same source, packet generation is usually assumed to be a succession of active and idle periods. Packet generation
Fig. 8. Comparison of the packet loss rates of MSN, MS4 and TBSF under hot spot traffic and full load for N 128 and h 0.5.
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Fig. 9. Comparison of the packet loss rates of MSN, MS4 and TBSF under MAXDT and full load for N 1024.
occurs only during active periods, and the packets generated during the same active period form a burst. The most popular traffic source model exhibiting this behavior is called the ON/OFF model which is simple and analytically tractable. The terms ON and OFF correspond to the active and idle periods, respectively. In BT, packets arrive at an input port in the form of bursts of random length such that all packets of a burst are destined to the same output port. BT is characterized by the distribution of burst length (i.e., the length of active period), the gap between consecutive bursts (i.e., the length of idle period), and the process describing the output port requests for bursts. We assume that the output port requested by all packets of a burst is chosen
uniformly among all output ports independently from all other bursts. The peak cell arrival rate, p, refers to the cell arrival rate when the source is in the ON state and is equal to 1/T, where T is the time between two consecutive cell arrivals during the ON period. In accordance with the recommendation by ITU-T, we assume that the active and idle periods are exponentially distributed with parameters a and b whose mean values are 1/a and 1/b, respectively. We also assume that the following three parameters are known for each source: (1) the average packet rate, denoted (m), that is equal to ( p × a ⫺1) / (a ⫺1 ⫹ b ⫺1), (2) the mean burst length in packets, (B), being equal to a ⫺1/T, and (3) the burstiness factor (b )
Fig. 10. Comparison of the packet loss rates of MSN, MS4 and TBSF under MINDT and full load for N 1024.
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Fig. 11. Comparison of the packet loss rates of MSN, MS4 and TBSF under an ATM traffic and full load for N 64.
that equals p/m. Each of active and idle periods can be taken either as exponential or a geometric random variable, based on the choice of time axis as either continuous or slotted, respectively. The parameters a ⫺1, b ⫺1, and T are known (packet interarrival time) can be calculated when the parameters m, B, and b of a source are known [10]. Once a ⫺1 and b ⫺1 are calculated, the exponentially distributed durations for active and idle periods in a given timeslot can be computed using the exponential distribution functions. Various traffic sources to be serviced by ATM networks belong to three main classes: (1) constant bit rate (CBR) sources (e.g., 64 kbit/s voice and fixed-rate video networks) which do not have any idle period in packet generation, (2) variable bit rate (VBR) sources such as file transfer, electronic mail, and terminal emulation in services of connectionless and connection-oriented data, and (3) VBR-video sources. We compared the packet loss rates of MSN, MS4, and TBSF under an ATM traffic in which the sources generate 20% video, 40% voice, and 40% data traffic. This ATM traffic is generated by using trace-driven simulation (i.e., the traffic of sources is first generated and, then, applied to each of three networks). Fig. 11 shows the packet loss rate against the number of stages for MSN, MS4, and TBSF under the ATM traffic for N 64. As seen from the figures, MSN exhibited lower packet loss rates than MS4 and TBSF. As N increases, the difference between packet loss rates of MSN and the switches MS4 and TBSF is expected to grow in favor of MSN.
4. Conclusion The challenge facing B-ISDN community has been to create an efficient high-performance ATM switch that can support existing and emerging services. Such a network
should route packets on the fly, provide switching of packets at a very high speed, and have acceptable packet loss rates and low hardware complexity. In this paper, we proposed a self-routing, low hardware complexity, banyan network based output buffering ATM switch called MSN. MSN improves the performance of banyan networks by reducing their internal conflicts. We also presented a fast destination tag routing scheme, FDR, for an output buffering ATM switch. FDR minimizes the number of stages that a packet has to be routed through to reach its destination. By running extensive computer simulations, the performance of MSN is compared with the performance of similar networks MS4 and TBSF under a variety of different traffic models such as uniform, hot-spot, output-concentration and ATM bursty traffic. Simulation results show that the packet loss rate of MSN is smaller than that of MS4 and TBSF. The performance of MSN has also been analyzed by an analytical model under uniform traffic. The analytical results closely match with the simulation results. Acknowledgements The author wishes to acknowledge the support provided by King Fahd University of Petroleum and Minerals. References [1] S.F. Oktugˆ, M.U. C¸agˆlayan, Design and performance evaluation of a banyan network based interconnection structure for ATM switches, IEEE Journal on Selected Areas in Communications 15 (5) (1997) 807–816. [2] D. Basak, A.K. Choudhury, E.L. Hahne, Sharing memory in banyanbased ATM switches, IEEE Journal on Selected Areas in Communications 15 (5) (1997) 925–937.
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A high-performance ATM switch based on modified shuffle-exchange network Hasan C ¸ am* Computer Engineering Department, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia Received 22 October 1997; received in revised form 11 September 1998; accepted 24 September 1998
Abstract This paper presents an output buffering ATM switch, called modified shuffle-exchange network (MSN) that is obtained by inserting a connection pattern just after every other shuffle-exchange stage. The purpose of modifying a shuffle-exchange network by inserting a connection pattern is to reduce significantly the number of its internal conflicts. Each link of every other stage of MSN has a filter to route successful packets to their destinations. Instead of employing the traditional destination tag routing scheme on MSN, we developed a fast destination tag routing scheme, called FDR, for MSN. In the traditional destination tag routing scheme, the routing tag of a packet is made equal to its destination address. In FDR, however, the routing tag of a packet is determined by its destination address as well as source address. FDR often requires less than log2 N stages to route a packet from its source to destination, which leads the traffic load to be reduced at the successive stages of the network. An analytical model is presented to analyze the performance of MSN under uniform traffic. Under a variety of traffic models, including uniform, hot-spot, ATM bursty, and output concentration, extensive simulations are run to examine and compare the performance of MSN with two existing similar networks. The simulation results show that MSN with FDR improves the packet loss probability substantially. 䉷 1999 Elsevier Science B.V. All rights reserved. Keywords: Shuffle-exchange network; Internal conflict; Destination tag routing scheme; Output buffering ATM switch; Performance evaluation
1. Introduction Fast packet switching technique such as asynchronous transfer mode (ATM) is considered to be the most appropriate switching technique for the transmission of voice, data, images and video in an integrated fashion. The challenge is to design and build packet switching networks capable of switching relatively small packets at extremely high rates [4]. Multistage interconnection networks (MINs) such as banyan networks are listed among the most desirable building blocks for fast packet switching networks. Among the main advantages of a banyan network are selfrouting, low hardware complexity compared to crossbar switch, distributed control, suitable for VLSI implementation, modular and scalable [1–3]. The main disadvantage of banyan networks is to have a limited number of connection patterns, which results in a significant number of internal conflicts in switching elements (SEs). To make banyan networks suitable for ATM switches, this paper presents a modified shuffle-exchange network (MSN) that has a much * Tel.: ⫹ 966-3860-2147; fax: ⫹ 966-03860-3059; e-mail: cam@ ccse.kfupm.edu.sa
smaller number of internal conflicts than a shuffle-exchange network. As MSN is an output buffering ATM switch with packet filters at the links of stages, a new self-routing algorithm, called fast destination tag routing scheme (FDR), is introduced to improve the performance. As the incoming traffic to a banyan network is usually not known in advance, multiple packets arriving simultaneously at different input ports may have to be forwarded along the same internal link. This leads to the main drawback of banyan networks, called internal conflict: two packets destined for different outputs of the network request simultaneously the same output link of a given SE. Another important problem that any MIN has to deal with is the output contention in which multiple packets are destined to the same output port. Both internal conflict and output connection severely degrade the throughput performance and the packet loss probability of a banyan network. To reduce the adverse effects of the internal conflict and output contention, one solution is to add extra stages to banyan network and provide output buffering, as in the tandem banyan switching fabric (TBSF) [4] and MS4 [5]. TBSF consists of K banyan networks in series. MS4 is constructed using K ⱖ n log2 N shuffle-
0140-3664/99/$ - see front matter 䉷 1999 Elsevier Science B.V. All rights reserved. PII: S014 0-3 664(98)00257 -6
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Fig. 1. A 7-stage MSN with 16 inputs/outputs. The odd-numbered and even-numbered stages of MSN are identical to the shuffle-exchange and a -exchange stages, respectively.
exchange stages, each with N/2 unbuffered SEs and N inputs/outputs. Outputs of stages n to K are also connected to the inputs of the same-number output port modules (OPMs) through filters. MS4 is motivated by the observation that those misrouted packets that are marked invalid in TBSF waste the switching resources because they are not allowed to re-start routing until the next banyan network. Therefore, similar to an earlier proposed ATM switch called rerouting network [6], MS4 starts rerouting a misrouted packet just after it loses contention. To achieve rerouting in MS4, each packet has a counter field (C) of dlog2 ne bits that is initially set to n. Whenever a packet successfully passes through a stage of MS4, its counter C is decremented by 1, and each time a packet loses contention its counter is reset to n. The proposed network MSN in this paper also starts immediately re-routing a misrouted packet, but FDR can set its counter to a number smaller than n depending on the minimum distance between the packet and its destination. This directly translates into higher throughput in MSN, since packets remain for little time within the network on average and therefore consume less network resources [7]. Also, filters in MSN are located at the output links of every other stage, which leads to a reduction in the hardware complexity. The traditional destination tag routing scheme is a selfrouting distributed-control procedure used to establish a path from any input port of banyan network to any output port. Specifically, to route a packet destined to an output port of banyan network, say d, with binary representation d1d2…dn (where d1 is the most significant bit), the destination routing scheme uses the destination address d1d2…dn as the routing tag for the packet. In the proposed FDR, the routing tag of a packet is determined by both its destination
address and source address, which usually leads the routing tag to have less than n bits. The rest of the paper is organized as follows. In Section 2, we introduce MSN and FDR. Section 3 presents an analytical model for MSN under uniform traffic, and compares the performance of MSN, MS4 and TBSF using simulation results under uniform and nonuniform traffic patterns. Concluding remarks are made in Section 4.
2. Architecture of MSN MSN is designed with the following goals in mind: 1. Reduce the number of internal conflicts that occur in the SEs of a shuffle-exchange network. 2. Whenever it is not possible to avoid having internal conflicts among four packets arriving at two SEs of a stage, route correctly those packets that are closest to their destinations. 3. Whenever a packet is misrouted (or deflected) to a wrong outlet of an SE as a result of conflict, first compute its new routing tag based on the minimum distance between the packet and its destination and, then, start immediately re-routing the packet. To achieve the first part of goal 3, we developed FDR to compute a new routing tag based on the minimum distance. To start rerouting immediately and easily, the stages of a network should be identical and, therefore, we have chosen shuffle-exchange network to realize the second part of goal 3. To accomplish goals 1 and 2, we introduce an a exchange stage that is inserted just after every other shuffle-exchange stage. These three goals together aim to
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Fig. 2. (a) Those control bits that would have conflicts on two SEs of a banyan network can be routed successfully through the SEs of a core network in MSN. (b) Any set of control bits that do not have conflicts on two SEs of a banyan network are also routed successfully through the SEs of a core network in MSN.
improve the network performance by preventing especially those packets that are very close to their destinations from being misrouted in case of a conflict, thereby increasing the number of successful packets and reducing the possibility of occurring conflicts in SEs of the successive stages. Let a denote a connection pattern such that, for 0 ⱕ i ⱕ N ⫺ 1; input i of the pattern is connected to output i or
Fig. 3. Algorithm SET-SE used for setting each switching element of MSN.
i ⫹ (N/2) mod N based on that i is even or odd, respectively. a -exchange is defined as being a stage consisting of the connection pattern a followed by a column of N/2 bitcontrolled SEs of size (2 × 2) each. As shown in Fig. 1, MSN is constructed by inserting an a -exchange stage just after every other shuffle-exchange stage, where each stage has N/2 unbuffered binary SEs. MSN stages are labeled from left to right starting with 1 up to K. The odd-numbered and even-numbered stages of MSN are identical to the shuffle-exchange and a -exchange stages, respectively. Any SE of an even-numbered (respectively, odd-numbered) stage is called even-SE (respectively, odd-SE). The outlets of every odd-SE are connected to the inputs of the same number OPMs through filters. As in TBSF and MS4, OPMs perform buffering and concentration functions. The SEs of each stage in MSN are labeled from top to bottom, starting with 0 until 2 n⫺1 ⫺ 1. For 0 ⱕ j ⱕ 2n⫺2 ⫺ 1, the jth and j ⫹ 2n⫺2 th SEs of each stage form a pair j. Thus, each stage has 2 n⫺2 pairs of SEs. Note that the four outlets of pair j of odd-SEs are connected to the inlets of pair j of even-SEs through the connection pattern a . These two pairs of odd-SEs and even-SEs are said to form a core-network with 4 inputs/outputs, as shown in Fig. 2. The odd-SEs of a core-network act somewhat like sorting cells introduced in [9] in the sense that their main function is to prevent even-SEs from having some conflicts. Therefore, the number of internal conflicts in MSN depends on how much a core-network is successful in preventing internal conflicts on its even-SEs. Let a and b (respectively, c and d) be the control bits of an odd-SE (respectively, the other odd-SE) of a core-network, where control bit refers to a destination address bit used in setting SE. If {a, b} {0,1} and {c,d} {0,1}, no conflict occurs in the even-SEs of the core-network similar to SEs of any banyan network, as shown in Fig. 2(b). But, if {a,b} {0,0} and {c,d} {1,1}, no conflict occurs in the even-SEs either, as shown in Fig. 2(a). Also note that some active packets arriving at inputs of a core-network may not reach any outlet of an even-SE of the network because filters at the outlets of odd-SEs may route them to OPMs because their counters are zero, which helps reduce the possibility of having internal conflict in even-SEs. Algorithm SET-SE, shown in Fig. 3, describes how to set both an even-SE and odd-SE, and shows when a filter extracts successful packets to their destinations. Each packet header in MSN comprises an activity bit a, its binary destination address d1 d2…dn, a counter field C of [log2 n] bits, and a conflict bit w. The activity bit a indicates whether an input receives a packet (a 1) or does not receive (a 0). Whether an SE will be set to cross or straight depends upon the activity bits (a u, a l), the counters (C u, C l), and the control u l u ⫹1 and d bits dn⫺C n⫺C l ⫹1 of the packets arriving at the inputs of the SE, where superscripts u and l stand for upper and lower, respectively, to distinguish the packets of the upper and lower inputs of an SE. In case of an internal conflict, the
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Fig. 4. The state transition diagram of a packet.
packet with smaller counter value is routed correctly because it is closer to the destination. If no packet arrives at the inputs of an SE of MSN, then no action is taken and the SE is left in its present state (line 1 of SET-SE). If one of the inputs of an SE does not receive a packet, the SE is set according to the control bit of the available packet (lines 2 to 3). If both inputs receive a packet and the control bits form the set {0,1}, then the SE does not have a conflict and is set accordingly (line 4.1). If SE has a conflict because the control bits of the packets are the same, then the packet with smaller counter value is routed correctly (lines 4.2 and 4.3); if the counter values are the same, then the packet to be routed correctly is selected randomly (line 4.4). Initially, all conflict (i.e., w) bits are reset to zero. Whenever a packet loses contention, its conflict bit is set to 1 (line 4.6). If the counter of a packet that is routed correctly in an odd-SE is less than or equal to 1, then the packet is distinguished and routed to its destination by a filter (line 6.2.1). If a packet reaches an outlet of an even-SE with a conflict bit of 0 (respectively, 1), then its counter is decremented (respectively, initialized by FDR), as shown in lines 6.1.1 and 6.1.2 of SET-SE. 2.1. FDR The destination tag routing scheme works in omega network as follows [8]. Assume that the stages of omega network are labeled in ascending order from left to right, starting with 1, and the outputs of each stage are labeled in m m ascending order from 0 to N ⫺ 1. Let im im 1 i2 …in and r r r r d d1 d2 …dn denote the input m and the output r, respectively,of omega network, where 0 ⱕ m, r ⱕ N ⫺ 1. Now, let us suppose that a packet, say A, arriving at input port i m is destined to the output port d r. The destination tag routing scheme initializes the routing tag of packet A to d r. If packet A does not encounter any internal conflict, stage k switches m m r r packet A from its input im k ik⫹1 …in d1 …dk⫺1 into the output m m m r r ik ik⫹1 …in d1 …dk for k, 1 ⱕ k ⱕ n. Thus, stage n finally switches packet A into the output port d r. The basic idea behind FDR is to eliminate the need for routing packet A through the first k stages if the following m m r r r and already holds: im n⫺k⫹1 in⫺k⫹2 …in d1 d2 …dk m m m r r r r in⫺k in⫺k⫹1 …in 苷 d1 d2 …dk dk⫹1 . After determining k, FDR r r dk⫹2 …dnr and initializes the routing tag of packet A to dk⫹1 sets the counter field C of packet A to n ⫺ k. As an example
for N 16, if a packet with destination address 1100 arrives at input port with address 0110, the value of k for the packet will be 3 because the last three bits i2i3i4 ( 110) of the input port address are the same as the first three bits d1d2d3 ( 110) of the destination address. So, the packet needs to be routed correctly through one stage only according to d4 0 and, therefore, the counter field C of the packet is initialized to 1. 2.2. Packet sequencing Assume that the last stage, stage K, of MSN is an old numbered stage. Let t s denote the maximum delay incurred at a SE of MSN, and T denote the packet duration in bit times. For an ATM packet, T equals 424 because any ATM packet has 424 bits. Assume that packets A and B are destined to the same output port, and packet B arrives in the same input port of MSN just after packet A. The worst case happens when packets A and B are successfully routed to OPMs by the filters of stages K and 1, respectively. This implies that packets A and B are considered successful after K.t s and T ⫹ t s bit times. If each OPM is assumed to be a FIFO queue such that the location of a packet is determined by the arrival time of its first bit, then the condition for preserving the order of packets A and B in the worst case is K.t s ⬍ T ⫹ t s or ((K ⫺ 1) t s / T) ⬍ 1. To satisfy this condition for large K, additional artificial delays can be inserted into those inputs of each OPM that are connected to the leftmost stages of MSN. 3. Performance of MSN The performance of MSN has been evaluated under different traffic models. A traffic model is determined by the destination request distribution of arriving packets, and the process describing the arrival of packets at the input ports of the network. The simplest traffic model is the uniform traffic in which the process describing the arrival of packets at the input ports is an independent and identically distributed Bernoulli process with the load parameter p (0 ⬍ p ⱕ 1). We assume that a packet arrives at a given input port in a given timeslot with probability p. As for the destination request distribution of arriving packets under uniform traffic, each packet chooses its destination port uniformly among all output ports, independently from all
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previous and current arriving packets. In evaluating the performance of a self-routing ATM switch, packet loss rate Ploss is usually more important than delay. Ploss, being the fraction of packets lost within the switch, is required to be lower than 10 ⫺6 in most ATM switches. In the comparison of switches, we assume that no packet is lost in any OPM. 3.1. Analysis of MSN In this section, the performance of MSN is analyzed under uniform traffic. We assume that packets arrive at the inlets of any (2 × 2) SE independently of each other, and a packet chooses a particular outlet of an SE with probability 1/2. A packet of MSN has n ⫹ 1 states labeled from 0 to n, where state i, 0 ⱕ i ⱕ n, represents that packet’s counter C equals i. The state transition diagram of a packet is shown in Fig. 4. In this diagram, the event of not having a packet at an input port with probability 1 ⫺ p is also represented by state 0. When a packet arrives at an input port or loses contention in an even-SE, FDR initializes its counter C to one of the numbers ranging 1 to n. As described in algorithm SET-SE, a packet with state i moves to state i ⫺ 1 with probability Wi in an even-SE. Thus, Wi is the probability that a packet wins in state i. Li refers to the ‘‘loss’’ probability of a packet in state i so that Li 1 ⫺ Wi. When a packet in state i loses contention, the probability that FDR initializes its counter to one of the states i, i ⫹ 1,…, n is Li/(n ⫺ i ⫹ 1). Let Qi(k) denote the probability that a link at stage k of MSN carries a packet with state i, for 1 ⱕ k ⱕ K, where K is the label of the last stage. This implies that Q0(k) represents all those packets that successfully reach their destinations prior to stage k. As the arrival process of any packet at MSN is assumed to be independent and identically distributed Bernoulli process with parameter p, the probability that an input port does not receive any packet is 1 ⫺ p, that is, Q0(1) 1 ⫺ p. To determine Qi(1) for the other i’s as well, let a denote the summation of all integers from 1 to n inclusive. As the counter C of a packet with destination address d1d2…dn is set to n ⫺ i at an input port address x1 x2 …xn by FDR if x1⫺i⫹1 …xn d1…di and xn⫺i xn⫺i⫹1…xn ^ d1…didi⫹1, we assume that Qi(1) ip=a. Let Qi(K ⫹ 1) denote the probability that an outlet of an SE at the last stage K carries a packet with state i. As any packet in a state other than state 0 that reaches an outlet of an SE at the last stage is lost, the throughput of MSN equals Qi(K ⫹ 1). The normalized throughput is given by Q0(K ⫹ 1)/p. Thus, the mean Ploss is equal to 1 ⫺ [Q0(K ⫹ 1)/p]. Let us consider a core-network shown in Fig. 2 where the even-SEs belong to an even-numbered stage r between 2 and K. The upper and lower inputs of an even-SE of the core-network are assumed to be labeled arbitrarily by X and Y. A packet, denoted A, with state i arriving at input X loses contention to a packet B arriving at input Y if and only if: packet B also requests the same outlet (this occurs with
probability 1/2) and either packet B has C i and is chosen to be winner by function random (u,l) (this occurs with probability Qi(r)/2) or packet B is closer to itsPdestination with 1 ⱕ C ⬍ i (this occurs with probability i⫺1 j1 Qj r). But, input Y is connected to an outlet of an odd-SE of the core-network and packet B is one of those two packets that arrived earlier at the inputs of the odd-SE. This implies that the probability that packet B requests the outlet of the oddSE connected to Y is 1/2. Consequently, each probability of conditions 1 and 2 is multiplied by 1/2. Thus, the loss probability Li(r) that packet A with state i loses contention to packet B is given by 2 3 ⫺1 141 1 i ⫺ 1 iX Q r ⫹ Qj r5 Li r 4 4 i 2 i j1 As Wi(r) 1 ⫺ Li(r), the probability Wi(r) that a packet with C i wins contention in an even-SE of stage r is computed by: ⫺1 1 i ⫺ 1 1 iX Q r ⫺ Q r Wi r 1 ⫺ 16 i i 8 j1 j We obtain from Fig. 4: Q0 r ⫹ 2 Q0 r ⫹ Q1 r·W1 r Qi r ⫹ 2 Qi⫹1 r·Wi⫹1 r ⫹
i X j1
1 ⫺ Wj r; Qn r ⫹ 2
n X j1
1 Q r n⫺j⫹1 j
1 ⱕ i ⱕ n ⫺ 1
1 Q r:1 ⫺ Wj r n⫺j⫹1 j
By solving these recursive equations for even integers r 2, 4, 6,…,K ⫺ 1, the mean Ploss which equals 1 ⫺ [Q0(K ⫹ 1)/p] can be computed for different values of n and K. 3.2. Simulation results Extensive computer simulations are run under different traffic patterns to evaluate and compare the performance of MSN, MS4 and TBSF. In all simulation results, any point has been obtained by averaging over ten independent simulation runs. A 90% confidence interval on the order of 10 ⫺7 was observed for packet loss rates in the 10 ⫺6 range. As packet losses that occur at OPMs are a function of the output buffer sizes and the main sources of packet losses are internal conflicts rather than output port contentions [4,5], the simulation results for the packet loss rate of MSN, MS4 and TBSF do not include those packet losses occurring at OPMs. 3.2.1. Uniform traffic In the simulations, the destination of each arriving packet at an input port is set randomly by a random number generator to simulate the destination request distribution function
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Fig. 5. The packet loss rates of analytical and simulation models versus the number of stages for different values of N at full load of MSN.
under uniform traffic. We first validate the analytical model of MSN against the results obtained by computer simulations. Fig. 5 shows the packet loss rate of analytical and simulation models as a function of K (the number of stages) at full load (p 1) for N 128 and N 1024, where the analytic results match closely with simulation results. Next, we compare the performance of MSN, MS4 and TBSF using simulation results. Figs. 6 and 7 compare the packet loss rates of MSN, MS4, and TBSF as a function of K for N 1024, at full load and half load, respectively. The number of stages required to achieve a low packet loss rate in MSN is lower than the number of stages required in MS4 and TBSF. This is an expected result because MSN reduces internal conflicts, compares the counter of a packet with
three other counters rather than just one counter in case that there is a conflict in a core-network, and employs FDR to minimize the number of stages that a packet should be routed through. 3.2.2. Nonuniform traffic 1. Hot-Spot Traffic (HST): When a large number of packets arriving at input ports are destined to the same output port, internal conflicts rapidly increase on the paths heading towards the destination and, therefore, the output port is called hot spot. The traffic directed at the hot spot is sometimes called hot traffic, and the remaining traffic is called cold traffic. HST occurs in many systems and reallife applications. For instance, in case of multiprocessors,
Fig. 6. Comparison of the packet loss rates of MSN, MS4 and TBSF under uniform traffic and full load for N 1024.
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Fig. 7. Comparison of the packet loss rates of MSN, MS4 and TBSF under uniform traffic and p 0.5 for N 1024.
many multiprocessors may request to access the same memory module. Let h represent the fraction of packets destined to the hot spot. We assume that hot spot and the destinations of cold traffic packets are chosen uniformly among all output ports. For N 128, Fig. 8 shows the packet loss rates of MSN, MS4, and TBSF versus the number of stages for h 0.5 at full load under HST. As h 0.5, N/2 packets are destined to a single output port and, therefore, packet loss rates are very high in the switches. 2. Output-Concentration Traffic (OCT): In this model, all arriving packets at input ports are destined to only a subset of all output ports. Assuming that the subset contains L output ports, the destination of a packet is
chosen uniformly among all L members of the subset. Two extreme cases of this model, namely maximum- and minimum-distance OCT (MAXDT and MINDT, respectively), are considered in [4, 5]. In MAXDT, the subset contains all N/2 odd-numbered (or even-numbered) output ports. In MINDT, the subset contains N/2 consecutive output ports (e.g., the upper half of the output ports). Figs. 9 and 10 compare the packet loss rates of MSN, MS4, and TBSF for N 1024 at full load under MAXDT and MINDT, respectively. 3. Bursty Traffic (BT): To capture the correlation in the time domain among packets originating from the same source, packet generation is usually assumed to be a succession of active and idle periods. Packet generation
Fig. 8. Comparison of the packet loss rates of MSN, MS4 and TBSF under hot spot traffic and full load for N 128 and h 0.5.
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Fig. 9. Comparison of the packet loss rates of MSN, MS4 and TBSF under MAXDT and full load for N 1024.
occurs only during active periods, and the packets generated during the same active period form a burst. The most popular traffic source model exhibiting this behavior is called the ON/OFF model which is simple and analytically tractable. The terms ON and OFF correspond to the active and idle periods, respectively. In BT, packets arrive at an input port in the form of bursts of random length such that all packets of a burst are destined to the same output port. BT is characterized by the distribution of burst length (i.e., the length of active period), the gap between consecutive bursts (i.e., the length of idle period), and the process describing the output port requests for bursts. We assume that the output port requested by all packets of a burst is chosen
uniformly among all output ports independently from all other bursts. The peak cell arrival rate, p, refers to the cell arrival rate when the source is in the ON state and is equal to 1/T, where T is the time between two consecutive cell arrivals during the ON period. In accordance with the recommendation by ITU-T, we assume that the active and idle periods are exponentially distributed with parameters a and b whose mean values are 1/a and 1/b, respectively. We also assume that the following three parameters are known for each source: (1) the average packet rate, denoted (m), that is equal to ( p × a ⫺1) / (a ⫺1 ⫹ b ⫺1), (2) the mean burst length in packets, (B), being equal to a ⫺1/T, and (3) the burstiness factor (b )
Fig. 10. Comparison of the packet loss rates of MSN, MS4 and TBSF under MINDT and full load for N 1024.
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Fig. 11. Comparison of the packet loss rates of MSN, MS4 and TBSF under an ATM traffic and full load for N 64.
that equals p/m. Each of active and idle periods can be taken either as exponential or a geometric random variable, based on the choice of time axis as either continuous or slotted, respectively. The parameters a ⫺1, b ⫺1, and T are known (packet interarrival time) can be calculated when the parameters m, B, and b of a source are known [10]. Once a ⫺1 and b ⫺1 are calculated, the exponentially distributed durations for active and idle periods in a given timeslot can be computed using the exponential distribution functions. Various traffic sources to be serviced by ATM networks belong to three main classes: (1) constant bit rate (CBR) sources (e.g., 64 kbit/s voice and fixed-rate video networks) which do not have any idle period in packet generation, (2) variable bit rate (VBR) sources such as file transfer, electronic mail, and terminal emulation in services of connectionless and connection-oriented data, and (3) VBR-video sources. We compared the packet loss rates of MSN, MS4, and TBSF under an ATM traffic in which the sources generate 20% video, 40% voice, and 40% data traffic. This ATM traffic is generated by using trace-driven simulation (i.e., the traffic of sources is first generated and, then, applied to each of three networks). Fig. 11 shows the packet loss rate against the number of stages for MSN, MS4, and TBSF under the ATM traffic for N 64. As seen from the figures, MSN exhibited lower packet loss rates than MS4 and TBSF. As N increases, the difference between packet loss rates of MSN and the switches MS4 and TBSF is expected to grow in favor of MSN.
4. Conclusion The challenge facing B-ISDN community has been to create an efficient high-performance ATM switch that can support existing and emerging services. Such a network
should route packets on the fly, provide switching of packets at a very high speed, and have acceptable packet loss rates and low hardware complexity. In this paper, we proposed a self-routing, low hardware complexity, banyan network based output buffering ATM switch called MSN. MSN improves the performance of banyan networks by reducing their internal conflicts. We also presented a fast destination tag routing scheme, FDR, for an output buffering ATM switch. FDR minimizes the number of stages that a packet has to be routed through to reach its destination. By running extensive computer simulations, the performance of MSN is compared with the performance of similar networks MS4 and TBSF under a variety of different traffic models such as uniform, hot-spot, output-concentration and ATM bursty traffic. Simulation results show that the packet loss rate of MSN is smaller than that of MS4 and TBSF. The performance of MSN has also been analyzed by an analytical model under uniform traffic. The analytical results closely match with the simulation results. Acknowledgements The author wishes to acknowledge the support provided by King Fahd University of Petroleum and Minerals. References [1] S.F. Oktugˆ, M.U. C¸agˆlayan, Design and performance evaluation of a banyan network based interconnection structure for ATM switches, IEEE Journal on Selected Areas in Communications 15 (5) (1997) 807–816. [2] D. Basak, A.K. Choudhury, E.L. Hahne, Sharing memory in banyanbased ATM switches, IEEE Journal on Selected Areas in Communications 15 (5) (1997) 925–937.
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