3 MATLAB Project In this project you are asked to analyze an M/M/1 packet queueing system with an arrival rate and servi

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3 Matlab Project In This Project You Are Asked To Analyze An M M 1 Packet Queueing System With An Arrival Rate And Servi 1 (264.9 KiB) Viewed 39 times

3 MATLAB Project In this project you are asked to analyze an M/M/1 packet queueing system with an arrival rate and service rate ji. 1. For i = 0.1 packets per millisecond and u = 0.125 packets per millisecond, use the formulae given in Section 2 to compute the mean (expected value) number of packets in the system, E[N(t)], and in the queue, E[N,(D], and the mean time spent by packets in the system, E[T], and in the queue, E[W] 2. To perform a computer simulation of this queueing system, log in to the course web page and down- load the MATLAB files exponentialrv.m and mml queue.m. Read the source code of the mmlqueue.m script; you will notice that it invokes the external function exponentialrv.m to generate random numbers that follow an exponential distribution. You will also notice that the mmiqueue.m script generates the arrival and departure processes for the M/M/1 queue as explained below. (a) The arrival process A(t) can be realized in either one of the following two ways: i. As a sequence of l's and 0's, where a l indicates the arrival of a packet. To do this, the time period of interest is subdivided into sufficiently small subintervals each of duration : so that at most one arrival can occur in any given subinterval. In this case, the sequence of l's and O's is a sequence of independent Bernoulli trials with success probability Ad. ii. Generate a sequence of random numbers from an exponential distribution with parameter to represent the interarrival times (time between successive arrivals). This was the approach taken in the coding of mml queue.m. (b) The departure process D(t) is generated as follows. Each arriving packet is served by the system; the service time is an exponential random variable with parameter f. At a given time, the system can only serve one packet (single-server system) on a first-come first-served basis. Additional packets must wait in the queue for service. If there are no packets waiting to be served, the server remains idle until the next packet arrives. c) Measure the following quantities: i. Number of packets in the system N(t) as the difference between the arrival and departure processes, i.e., N(t) = A(t) – D(t). Consider a time resolution of 1 ms. ii. The time spent by the ith packet in the system t; = tA; - tp;, where tĄ; is the arrival time of the ith packet and tp, is the departure time of the same packet. (d) Plot the following for a simulation time period of 200 ms (200 points): i. The arrival process Aſt) and the departure process D(t) vs. time on the same graph. ii. The number of packets in the system N(t) vs. time. iii. A graph of the total time t; spent by the ith packet vs. its arrival time tA;. For your reference, sample graphs produced by mmlqueue.m are shown in Figures 1 and 2.