lecture 8 hand simulation

Hand simulation:
The machine interference problem let us consider a single server queue with a finite population known as the machine interference problem. This problem arose originally out of a need to model the behavior of machines. Later on, it was used extensively in computer modeling. Let us consider M machines. Each machine is operational for a period of time and then it breaks down. We assume that there is one repairman.
Figure 1: The machine interference problem.
For simplicity, we will assume that the operational time of each machine is equal to 10 units of time. Also, the repair time of each machine is equal to 5 units of time. In other words, we assume that all the machines have identical constant operational times.
They also have identical and constant repair times. (This can be easily changed to more complicated cases where each machine has its own random operational and repair times.)
In this problem, the most important status variable is n, the number of broken down machines, i.e., those waiting in the queue plus the one being repaired. If n=0, then we know that the queue is empty and the repairman is idle. If n=1, then the queue is empty and the repairman is busy. If n>1, then the repairman is busy and there are n-1 broken down machines in the queue. Now, there are two events whose occurrence will cause n to change. These are:
1. A machine breaks down, i.e., an arrival occurs at the queue.
2. A machine is fixed, i.e., a departure occurs from the queue.
The flow-charts given in figures 2, show what happens when each these events occur.
Modeling & Simulation- Lecture -8- 17/12/2014
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