Analytical Modelling of Multistage ATM Switches with Backpressure Control Schemes

Performance modelling of Asynhronous Transfer Mode (ATM) switching is an active research area in high-speed communication. This paper presents a Markov modelling framework for analyzing a shared buffer ATM multistageinterconnection network (MIN) under a variety of buffer management and backpressure schemes proposed by other researchers and by the authors. A standard iterative computation approach is used to solve the steady-state probabilities. The analytical results are shown together with the simulation results, comfirming the usefulness of each backpressure scheme. Consequently, the results show that cell loss can be reduced when several backpressure schemes are combined together with pushout, as compared to a single conventional backpressure scheme. 1.0 Introduction Asynchronous Transfer Mode (ATM) has been proposed by the ITU-T as the principal technology for broadband switching. The key to success consists of its statistical multiplexing and its large bandwidth capability for supporting a wide varity of communication services. However, congestion control is still a big issuse that needs to be resolved prior to the ubiquitous deployment of ATM networks. In order to achieve the best possible performance from an ATM network, a comprehensive set of congestion control mechanisms should be applied all over the switching system. Some of the well-known congestion controls, such as Connection-Admission-Control, Windowing and Rate-based Congestion Control which operate on the high level of an ATM network have been studied extensively in the past literature [0]. They are known as node-to-node congestion control techniques that usually operate among the ATM switches and/or near the entrance of the switches. However, the low level congestion controls that function inside an ATM switch, have not been investigated in depth yet. The core of an ATM switch hardware is the switch fabric. This is made up from similar basic switching building elements (SEs), interconnected in a specific topology. Banyan network is a popular architecture for MIN implementation because it is simple and posesses attractive features (such as modularity which makes the switch suitable for VLSI implementation). The main problem of a Banyan network is internally blocking. Thus buffering is usually required in Banyan network to control the cell loss. Among all the buffering technqiues, shared buffering has the best performance aspects (high throughput and low cell loss probability) [1]. However, shared buffer SEs are prone to severe congestion due to monopolization of the buffer by favoured cells, especially under bursty traffic [2]. Bursts of cells may come simultaneously from more than one input and cells within a burst are likely to address the same output. If the mean burst length is long enough, the buffer will overflow. The congestion problem certainly aggravates in MIN because path contention intensifies when the SEs are blocked. The merits of shared buffer SEs and buffered MINs will diminish under bursty traffic unless some congestion control schemes are implemented. Some of the most effective lowlevel congestion controls are buffer management and backpressure flow control that operate in SE and in MIN respectively. These two techniques usually function together and are implemented in the same switch fabric. We concentrate on these low level congestion controls in this research work. At the SE level, buffers are often used to increase throughput and resolve output port contention for which the service of a cell must be delayed. But the performance of shared buffer SEs degrades dramatically under bursty traffic. To overcome this, restricted types of sharing and Hot-SpotPush-Out (HSPO) have been proposed, and the latter was demonstrated to be the best buffer management policy compared to others under bursty traffic in [2]. It is also proved mathematically to be an optimal scheme in [3]. At the MIN level, several types of backpressure schemes have been proposed for congestion control, and they have been evaluated extensively. In the general backpressure method, a congested SE informs the upstream SEs of its congestion status to grant/withhold cell transmission. This can be done either locally (LBP) or globally (GBP). Modified versions of backpressure such as RBP, suggested recently [4], and IBP proposed here, are described in a later section. 1.1 Previous Research on Backpressure A short survey of most backpressure schemes are given in Tables 1 and 2. Previous research results show that using either backpressure or pushout alone on MINs does not yield the best performance. However, most of the literature in the past concerns the study of one or two backpressure schemes. Pattavina et al. compared GBP and LBP in uniform traffic [5] and bursty traffic [6]. Saleh and Atiquzzaman also did the same in [7]. Recently, Choudhury and Hahne [4] proposed some innovative backpressure schemes, known as RBP (restricted backpressure with a Threshold) and Delayed-Pushout (which has pushout and RBP combined). They demonstrated that those schemes outperformed the conventional ones via simulations with bursty traffic. Oie et al., in [11] have done a preliminary performance analysis on backpressure controls with and without pushout, but their work is limited to a network of 2 stages, and uniform traffic is assumed. Dewar, in [18] compared combinations of GBP, LBP, Cut-through Routing and Speed-up, on Shared Buffer Banyan Networks with a Hot/Cold Traffic model, but the input load is uniform. It is now well-known that uniform traffic gives optimistic results because it does not represent a realistic traffic environment. To the best of our knowledge no one has provided an analytical model for all the available schemes under bursty traffic. However, a comparison of all the backpressure schemes is done by simulation in [19]. Also a new scheme called Intelligent Backpressure which is a variant of GBP is proposed there. The study in [19] showed that combining backpressure schemes with pushout is a very promising approach for shared-buffered MINs, but it was done using simulation only. An analytical model for all the backpressure control schemes is still lacking for performance analysis of shared-buffer MINs. 1.2 Objective The objective of this paper is to provide a performance analysis of most popular backpressure control schemes, to identify the advantages and weaknesses of each one of them, and to propose some new schemes which are combined with the optimal buffer sharing scheme. In particular, we present an analytical model for a number of the available backpressure schemes designed to improve the performance of shared buffer multistage ATM networks (or Banyan networks). The analysis is done by simulation as well as done by a discrete time Markov Model, that is developed for the first time to model most of the backpressure control schemes including pushout. 2 Assumptions Some assumptions are made for the analytical model under study, regarding the structure and operation of the Banyan network and the bursty traffic model. 2.1 Network Assumptions The network model under study is a N×N Banyan MIN and consists of n = logbN stages of SEs where each SE is a b×b shared buffer switch, and N is the number of inlets or outlets of the network. Let the number of SEs that each stage accommodates be m = N/b. Each SE is an bxb nonblocking ATM switch and all output ports share a central buffer of capacity B cells. Virtually there are b queues of cells, and each queue belongs to a unique output port, and they may grow to different lengths provided that their total is less than or equal to B. The network is operated synchronously in a discrete time slot basis, i.e. the cells are submitted to, and forwarded through the SEs in each stage at the beginning of constant time intervals. Every output port will select the cells for transmission from its own queue in a FIFO manner. The service time of a cell is assumed to be equal to one time slot. The enqueueing and dequeueing of cells in a buffer take place between two synchronization points. The flow of cells in the MIN is on a per cell basis. This means a destination tag is used to route a cell through the network. It is a n-tuple of information generated for each cell before it enters the network. Details of the MIN operation and details of the SE operation can be found in [7] and [14, 15, 16] respectively. 2.2 Bursty Traffic Assumptions A simple two-state ON/OFF Markov chain [20] is adopted to represent the bursty cell arrival process on each MIN inlet. Cell arrivals on the inlets of the MIN are generated by N independent sources with identical statistical characteristics. All the cells arriving on an inlet and belonging to the same burst, carry the same destination tag and travel the same links through the stages. For the bursty traffic model, the destination is chosen independently of other bursts and of the inlet on which the burst is arriving, and all destinations are equiprobable with probability 1/N. The destinations are uniformly distributed between bursts so that all outlets receive an equal number of cells on average. Mathematically, we describe here an ON/OFF bursty source with the two parameters, L which is the burst length, and p which is the offered load, so that the transition probabilities from the ON state to the OFF state, and from the OFF state to the ON state are t L 10 = 1 and t p L p 01 = ( ) ⋅ A respectively. 3 Congestion Control Methods 3.1 Global Backpressure (GBP) Under a backpressure control, congested SEs give no permission to upstream SEs for cell transmission, and hence stop receiving further cells from them until their buffer occupancy reduces. A request signal (which may be a SE identity from 0 to m-1) is sent downstream by the SE for each non-empty logical queue; a SE receiving nreq (up to b) requests, in which the number of cells that can be accepted in that time slot is ngrant, grants min(nreq, ngrant) requests by returning upstream acknowledgment signals. If ngrant < nreq, then the SEs to be granted are chosen at random. There are two common types of backpressure schemes, Global backpressure (GBP) and Local backpressure (LBP). Readers are refered to [5] for details. Though LBP is favoured for its simplicity in implementation, its performance is far worse than that of GBP [5], so we exclude the LBP scheme from our investigations. 3.2 Restricted Backpressure (RBP) Choudhury [4] proposed Restricted Backpressure (RBP) which allows backpressure to only part of the buffer. SEs upstream obey the rule of backpressure in sending the cells to downstream SEs when grants are received, as long as the content of the buffer is less than a threshold, T. Once the content of the buffer reaches T, the output ports of that SE will ignore any backpressure signals they may receive, and continue cell transmission even if the cells cannot be accepted by the downstream SEs and get lost. Hence buffers are always guaranteed to have at least B-T free spaces plus the cells that can go downstream, so traffic flow is not halted. 3.3 Intelligent Backpressure (IBP) This is a new backpressure scheme proposed in [19]. IBP is a modification of GBP. In IBP, the number of cell transmission grants to be sent to the requesting upstream SEs are chosen according to the number of cells in their buffers. When ngrant < nreq, grants are selectively given to the SEs who have the most congested buffer in order. That is, the first grant is given to a SE in which the number of cells is the greatest among the others, then the next grant is given to another SE which has the second most number of cells and so on until ngrant grants run out. The IBP scheme can be realized in implementation by assuming that the requesting information that is sent from the upstream SEs contains the SE identity as well as the number of cells currently stored in the buffer, so the receiving SE can build a sorted list identifying who requires to be granted most urgently. Processing overhead should not be much more than that required in any backpressure mechanism, since it would have to keep track of which upstream SEs have requested to send anyway. The idea of IBP is that grants are always given to SEs most requiring cell transmission, and hence, hopefully, cell loss is reduced and overall traffic flow is improved. 3.4 Hot-Spot Pushout (HSPO) The buffer management scheme called Hot-Spot Pushout (HSPO), features a dynamic cell purging mechanism used to drop cells from the longest queue in the buffer, to make room for an incoming cell when the buffer is full. Any one of the queues may become the longest queue from time to time. It all depends on the number of cells in the other queues and the bursty arrival. HSPO is used for relieving traffic congestion by balancing the length of each output queue in sharing the whole buffer. In contrast to the pushout that is commonly used for adjusting cell loss for different traffic classes, HSPO tries to improve throughput of a SE while keeping fairness in sharing the buffer. So the buffer is prevented from being hogged by any output queue. If an arriving cell which is destined to port i finds the buffer full, and port j has more cells in the buffer than any other port, HSPO functions as follows: In case i ≠ j, one of the cells tagged for port j is purged from the buffer in order to make room for the new cell to come. In the case where i = j, the arriving cell is dropped. 3.5 Combined Backpressure and Pushout HSPO (or PO in short), RBP and IBP all have their own special characteristics. They are the functions that control different aspects of MIN and SE. All these functions can be combined independently to form PO+RBP, PO+IBP and PO+IRBP. PO+IRBP is a new scheme that combines all the three functions, to improve traffic flow in different areas. Making all these schemes function simultaneously together should yield certain processing overhead, but the complexity in implementation is beyond the scope of this paper. 4 Analytical Model We analyse the backpressure schemes on a 4-stages 4×4 shared buffer Banyan network (which are typical MINs for ATM), in the presence of bursty traffic. The MIN is modelled by assuming that each SE in a stage is identical, since the SEs in a particular stage are statistically indistinguishable. Hence the state of a stage can be represented by the state of an SE in the stage. 4.1 Switching System Modelling Assuming a synchronous operation, as mentioned in 2.1, the behaviour of the whole network is modelled by the discrete time Markovian approach. The SE state is characterized by the content of a specific logical queue in the shared buffer, referred to as the tagged queue, and the cumulative content of the other b-1 logical queues, referred to as nontagged queues. In addition to that, the states of the loading sources for the tagged queue and the non-tagged queues are also considered together with the buffer content. Let the state of the system be represented by a 4-tuple s = (sq, sQ, sb, sB). S denotes the set of all the system states and j, m are the ‘state indices’ such that j, m ∈ S. sq and sQ are the number of cells in the tagged queue and the cumulative number of cells in the b-1 nontagged queues, whereas sb and sB represent the number of busy sources loading the tagged queue and the untagged queues respectively. The total number of cells stored in the buffer in state j is so(j), where so(j) = sq(j) + sQ(j) ≤ B. For simplicity, we let the number of tagged cells and untagged cells arrive be xq = sq(m) sq(j), and xQ = sQ(m) sQ(j) respectively. Also let the number of tagged cells and untagged cells depart be yq = sq(m) sq(j), and yQ = sQ(m) sQ(j) respectively. For a multistage network, a subscript i (1≤i≤n where n is the number of stages) is added to every variable. So for instance, the state of the system st becomes si,t for multistage network, meaning that state of a SE in stage i at time t. Since a Banyan network is symmetrical, one SE is used to represent all the SEs in a stage. So we require only n SEs to model the whole MIN. 4.2 Steady State Distribution The state equations for the MIN are defined as: