Question

In R Programming

1. The simulation of an M/M/1 Queuing System uses the service rate of 1.0 and the arrival rate of 0.5 to find the mean waiting time as described in Section 7.8.3. You need to change the “print() statement” at line 60 on page 169 to a return statement of the mean waiting time. You can develop three independent R scripts to answer the following questions.

1. If the arrival rate is always 0.5, draw a graph using the plot(serviceRate, meanWaitTime) function to illustrate the relation of mean waiting times with a given range of service rate from 0.5 to 1.5 with the increment of 0.1.

2. If the service rate is always 1.0, draw a graph using the plot(arriveRate, meanWaitTime) to illustrate the relationship of mean waiting times with a given range of arrival rate from 0.3 to 0.8 with the increment of 0.1.

3. Draw a 3D graph using the service rates (x axis) from 0.5 to 1.5 with the increment of 0.1; and the arrival rate (y axis) from 0.3 to 0.8 with the increment of 0.1 unit; and the mean waiting time as the z axis. You may use the function wireframe() in the library of lattice as in the section of 12.4 of our textbook to draw the graph. You have to develop a driver function to implement the simulation. You may use a text file, if you so choose, to store the collected data before your use wireframe() to display the 3D graph. But, this is not required.

Answer 1

Given , in  the simulation of an M/M/1 Queuing System ,

service rate = 1.0 and

arrival rate =0.5

We need to find the mean waiting Time.