M/M/1 queue with Comnet III

An M/M/1 queue is a single server queue with infinite buffer space, Poisson input traffic, and exponentially distributed service time. More specifically, the interarrival time between successive arriving packets is exponentially distributed with mean 1/ seconds, the packet size is exponentially distributed with mean 1/ bits. With the link capacity of C bps, the service time of each packet is exponentially distributed with mean 1/(C). We are interested in finding the average time that packets spent in the system.

  1. Drag and drop message source, processing node, point-to-point link, and network device icons on the left panel into the workspace and connect them together in series. Then, right click on each icon and go to properties… Rename the above icons to traffic generator, server, link, and sink respectively.
  1. Right click on traffic generator and go to properties… At Scheduling tab, set Interarrival to Exp(0.02). This means the packet interarrival time has an exponential distribution with mean 1/ = 0.02 seconds. At Messages tab, set Prob distrib to Exp(125), which means that the packet size has an exponential distribution with mean 1/ = 125 bytes. At Destinations tab, set Destination type to Weighted list. Press Edit Destination List -> Add, and then choose sink.

  1. Right click on traffic generator and go to statistics… Set Message Delay to ON by going to Edit and choose Collect stats.
  1. Right click on link and go to properties… At Link tab, set type to Point-to-Point and parameter to 56 kbps.

  1. Next, we specify the run parameters such as the length of warm up period, simulation time, the number of replications, etc. Go to Simulate -> Run Parameters… At Replications tab, set Warmup length to 5 seconds, Number of replications to 5, and Replication length to 50 seconds. Also enable Warmup every replication and Reset system every replication. At Statistics tab, set Confidence interval alpha to 0.1 and enable Export stats after run.

  1. Save the model and name it to mm1.c3. Start the simulation by pressing .
  1. After the simulation is done, right click at traffic generator and go to statistics… Highlight Message Delay and press View. You will see the statistics of message delay of each run in detail, including min, max, mean, standard deviation, and the confidence interval. In the Rep column, the Cumulative row displays the statistics of average message delay from 5 replications.

From the simulation, we get the average system time of 0.1681 seconds. The theoretical value of the average system time for an M/M/1 queue is given by 1/(C - ) = 0.167, which validates our simulation model.