ON/OFF Pareto Distributed Source At Burst Level: A Study Of Fast Simulation Methods For Packet Network S. H. S. Ariffin, J. A. Schormans Department of Electronic Engineering, Queen Mary University of London, Mile End Road, London E1 4NS. [email protected] Abstract Fast simulation is a method to decrease the computing time in simulations for network performance purposes. Faster analysis feedback and lower cell lost probability can be obtained. Modelling the source traffic at burst level will not only reduce the number of events to be simulated but also it will allow simulation of larger bandwidth network which require excessive computing resources. Hence, this paper overview an alternative method of fast simulation using ON/OFF source at burst level with Pareto distribution. Introduction The rapid growth in the use of telecommunication networks has called upon new technology to upgrade the speed of transmission without losing essential data. The third generation of communication (i.e. UMTS) must be reliable to support variety types of services to satisfy the needs of various types of customers. High-speed transport mechanisms, for example ATM, enable technologies for new classes of communication services such as multimedia and video-on-demand that are typically grouped under the heading of broadband ISDN (B-ISDN). High quality-of-service (QoS) networks require low probability of loss that sometimes is impractical to analyse analytically. Analytical models often need many assumptions, which are too restrictive for most real world systems. Simulation modelling however imposes fewer restrictions on the system in study. In order to simulate real loads into the network, longer computing times are required, where most published simulated results are unable to produce loss probability of 10-7 or below. New methods have been studied to accelerate the computing time of network simulations so that fast feedback and can be obtained [1-4,7,8,11,12]. Three methods in achieving this goal is by using a) more computing power [7] (i.e. parallel processing), b) statistical technique [8], c) or decompose the simulation model into connection, burst and cell scales [1-4,7,9,11,12] However this paper will concentrate on the third method. While modelling real-time traffic such as voice and image we use the ON/OFF traffic model, which represents bursty sources that have active periods and silent periods. The distribution of the active periods is often assumed to be exponential because of their relative mathematical simplicity combined with proven accuracy. However recent findings has discovered self-similarity and long-range dependence in a variety of types of source traffic [6]. A self-similar process has a tail probability that decays as a power law rather than exponentially. In order to analyse the impact of a traffic having this type of distribution, the Pareto distribution is used to represent the heavy tail network traffic streams.

The goal of this paper is to overview the fast simulation at burst level with ON/OFF Pareto distribution. The first section deals with the traffic model, the second section overview the cell rate fast simulation and the last section is the conclusion.

2 ON/OFF Pareto Distributed: Burst Source A traffic model that uses a bursty source manipulates a fixed cell rate period rather than the arrival or service times of a cell. In our models the distribution of the number of cells in both the ON and OFF periods is Pareto distributed where it generates cells at a peak cell rate (pcr) in active (ON) periods. In idle periods no cells are generated. In cell rate simulation an event is a burst of a fixed cell rate, followed by a change either to another period of ON duration or change to an OFF state and this is shown in Figure 1 where it implies mixing more than one ON/OFF source. The mean duration of an ON and OFF period is denote by Ton and Toff respectively. Bursty traffic would have Ton << Toff or Ton/ Toff << 1. Hence the mean number of cells produced in an active period is, (1) E on = Ton ⋅ (R − C ) Mean number of empty time slots during the silent period is E off = Toff ⋅ C (2) where R is the actual arrival rate and C is the actual cell service rate. For Pareto distribution process the actual mean duration of ON and OFF time is given by E on M on = (3) Eon − 1 E off M off = (4) Eoff − 1 and the probability that the source is active is

α=

Burst of cells

Ton Ton + Toff

(5)

OFF period

Events Figure 1: An event is mark by the change of cell rate of the ON periods or to OFF periods

Assuming that in one burst, cells are generated continuously rather than periodically, then for a single burst source, the flow of the traffic through a queue is described by input, output, queuing and loss cell rate (Figure 2). These rates are denoted by I( i, e), O( i, e), Q(i, e) and L(i,e) respectively where i indicates the ith virtual channel (VC) and e indicates the eth event at the queue. At any time, these the arriving cells are either serve, queue or loss, hence I (i, e) = O (i, e) + Q (i, e) + L(i, e)

(6)

where i = 1,…N e = 1,….. N is the maximum number of source that the switch can handle. Multiplexing of bursts from different sources through a buffer has to consider the simultaneous nature of these bursts. Bursts from different sources can affect the output rate of other VC passing through the buffer hence, I tot (e) = Otot (e) + Qtot (e) + Ltot (e) (7) where Itot(e) is the total input rate of all connections at event eth of the queue. N

I tot (e) = ∑ I (i, e)

(8)

i =1

Similar definitions apply for Otot(e), Qtot(e) and Ltot(e). Queue Input

Output

Cell loss

Figure 2: The queue modelling

3 Cell Rate Fast Simulation

Acceleration of simulation is essential in analysing network performance and traffic issues, and by decomposing the traffic model into burst scale and cell scale we can reduce the number of events to be processed, and therefore increase speed in the simulation. Recent studies have shown that using burst scale queuing, better cell loss probability estimates are obtained compared to cell-scale queuing as the buffer size increases [5,10]. Cell rate simulation is a burst-scale accelerates technique for modelling queuing behaviour. The burst level modelling approach allows network performance such as delay and cell loss probability to be measured, and this is essential to network that support real-time application such as voice and image. At the

burst level, the inter-arrival times of cells (or packets) are assumed constant, hence the source of the network need to produce a series of cells to mark an event of the burst. For a network to simulate many sources of traffic bursts, the total input rate needs to be considered in order not to overwhelm the output rate of the buffer. Thus the state of the queue in the buffer at any time has to be taken into account. In figure 3 three sources are multiplexed into a network and each has its own cell rate and ON time duration. In order to apply the equations in section 2, the total cell rate of each connection is sum up and compare with the service rate. This way the state of the queue can be determined and the cell loss probability will be obtained.

R1 Source1 time R2 1st event

2nd event Rtot1=R1+R2+R3

Rtot2=R1+R2+R3

Source2

Into the buffer

time R3

time 1st event

2nd event 1st event

Source3

2nd event

time 1st event

2nd event

Figure 3:Burst of cell from different connections There are three states of queue need to be consider which are •

•

•

I tot (e) < O(i, e) o C(i ,e) = 0 ; queue size is empty o I (i, e) = O(i, e) I tot (e) > O(i, e) o C (i, e) ↑ o Otot (e) = C tot (e) Queue is full o Ltot (e) = I tot (e) − Omax

4 Conclusions

This paper had overview an alternative way in modelling ON/OFF source traffic in order to accelerate a simulation, which is using burst scale queuing. It had also presented a distribution that matches heavy-tailed characteristics in network traffic streams by using Pareto distribution for the arrival of the ON/OFF sources. Besides enhancing the computing time, burst level modelling can also be use to analyse the

queue size and end-to-end performance such as the loss rate probability. So far burstscale and hybrid simulation/analysis technique have shown great promise [11, 12]. Our future work will be based on fast simulation using ON/OFF Pareto distributed source at burst level, which will analyse the impact of this type of source to the network performance.

Reference

[1] E. Lie, J. A. Schormans, L. Cuthbert and G. Stoneley, ‘A novel fast simulation method for ATM Network’, Proceeding of IEEE Conference on High Performance Switching and Routing 2000. [2] F. Hao, I. Nikolaidis and W. Zegura, ‘Efficient Simulation of ATM Networks with Accurate End-to-End Delay Statistics’ IEEE Int. Conference on Comm. 1998 (ICC98) Vol. 3. [3] J. M. Pitts, ’Cell-Rate Modelling for Accelerated Simulation of ATM at The Burst Level’, IEE Proceedings in Communication, Vol. 142, No. 6, Dec. 1995. [4] I. Nikoladis, R. M. Fujimoto and A. Cooper A., ‘ Time Parallel Simulation of Cascaded Statistical Multiplexers’, Pro. Of 1994 ACM SIGMETRICS Conference on measurement and Modelling of Computer Systems, May 1994. [5] J. W. Roberts, ‘ Variable-Bit-Rte Traffic Control in B-ISDN’, IEEE Communication Magazine, Sept. 1991. [6] P. Jelenkovic and P. Momcilovic, “Capacity Regions For Network Multiplexers With Heavy Tailed Fluid On-Off Sources”, INFOCOM 2001, IEEE Proceedings, Vol.1. [7] Bocci, M.; Pitts, J.M.; Cuthbert, L.G., “Exploiting Concurrency Through Knowledge Of Event Propagation In Cell Rate ATM Simulation”, Twelfth UK Teletraffic Symposium (Digest No. 1995/054), IEE , 1995. [8] M. Villen-Altamirano and J. Villen-Altamirano, “ RESTART: A Straight Forward Method for Fast Simulation of Rare Events”, Simulation Conference Proceedings, 1994. Winter. [9] Srinivasa Rao, T.; Bose, S.K.; Srivathsan, K.R.,” A Study On Call-Level Output Process Of An ATM Switch With Distorted On/Off Sources As Input “, TENCON '98. Volume: 1, 1998. [10] J.M. Pitts and L.G. Cuthbert, “ Fluid-Flow Theory Validation Of Cell Rate Simulation Technique For ATM-Based Broadband Networks”, Electronic letters February 1994, Vol. 30, No. 3. [11] J. Schormans, E. Liu, L. Cuthbert and J. Pitts, ‘ A Hybrid Technique For The Accelerated Simulation Of ATM Networks And Network Elements’, ACM Transaction on Modelling and Computer (TOMACS) Vol. 11, Issue 2, April 2001. [12] A.H.I. Ma and J. Schormans, ‘Hybrid Technique For Analysis Of Multiplexed Power-Law Traffic In Broadband Networks’, Electronics Letters, Vol. 38, No. 6, March 2002.