Problem 6 M/M/1 Queue A communication link capable of transmitting at a rate of
ID: 661363 • Letter: P
Question
Problem 6 M/M/1 Queue A communication link capable of transmitting at a rate of 50 Kbps is used to accommodate 10 sessions each generating Poisson traffic at rate 150 packets/minute. Packet are buffered until they can be transmitted. Assume packet lengths are exponentially distributed with mean 1000 bits. 1. Assume that the transmission capacity is divided into ten 5 Kbit/sec links and one link is assigned to each user. What is the average number of packets that are buffered? What is the average number of packets in the system (buffered and being transmitted)? What is the average delay per packet (buffer delay and transmission delay)? 2. Repeat part (1) but assume that packets from all sessions are served first-come first-serve using the entire transmission capacity (i.e., statistical multiplexing).Explanation / Answer
1. For each sesssion the arrival rate, l = 150/50 = 3 packets/sec
When the line is divided into 10 lines of capacity 5Kbit/sec, the average transmission time is 1/u=1/5 secs.
The corresponding utilization factor, p=l/u= 3/5 = 0.6
We have for each session Nq=(0.6)2/(1-0.6)= 0.9 and N=0.6/(1-0.6)= 1.5
T=1.5/3=0.5 secs for all sessions collectively Nq and N multiplied by 10 to give Nq=9 and N=15
2. When statistical multiplexing is used, all sessions are merged into a single session with 10 times larger l and u;
l=30, 1/u= 1/50.
We obtain p=0.6, Nq=0.9, N=1.5 and T= 1/20 secs. Therefore Nq,N and T have been reduced by a factor of 10 over the TDM case.