In Example 13.4 of section 13.5, we examined whether an M/M/1 system with a single fast server is better or worse than an MMs system with several slow servers. Keeping the same inputs as in the example, use simulation to see whether you obtain the same type of results as with the analytical models. Then repeat, using gamma-distributed service times with standard deviation six minutes.

Example 13.4 COMPARING ONE FAST SERVER TO SEVERAL SLOW SERVERS

Which system has the better steady-state characteristics such as L, W, LQ, and WQ: a single-server system where the single server can serve 30 customers per hour or a five-server system where each of the servers can serve six customers per hour? For each system, we assume that customers arrive according to a Poisson process at rate 25 per hour.

Objective To see whether customers should prefer a system with one fast server or a system with several slower servers.

Example 13.5

INCREASINGLY LONG LINES AT COUNTY BANK

Over a period of time, the County Bank branch office from Example 13.3 has been experiencing a steady increase in the customer arrival rate. This rate has increased from the previous value of 150 customers per hour to 160, then to 170, and it is still increasing. During this time, the number of tellers has remained constant at six, and the mean service time per teller has remained constant at two minutes. The bank manager has seen an obvious increase in bank congestion. Is this reinforced by the MMs model? What will happen if the arrival rate continues to increase?

Objective To see what happens to congestion in a multiple-server system when the traffic intensity gets close to 1.