Suppose a service facility consists of two stations in series (tandem), each with its
own FIFO queue. Each station consists of a queue and a single server. A customer
completing service at station 1 proceeds to station 2, while a customer completing
service at station 2 leaves the facility. Assume that the interarrival times of customers
to station 1 are IID exponential random variables with a mean of 1 minute. Service
times of customers at station 1 are exponential random variables with a mean
of 0.7 minute, and at station 2 are exponential random variables with mean 0.9
minute. Develop an Arena™ model for this system using the STATION and ROUTE
modules.
(a) Run the simulation for exactly 20,000 minutes and estimate for each station the
expected average delay in queue for the customer, the expected time-average number of customers in queue, and the expected utilization. In addition, estimate the
average number of customers in the system and the average time spent in the
system.
(b) Use the results of queuing theory to verify and validate your results for
part (a)
(c) Suppose now there is a travel time from the exit of station 1 to the arrival to
station 2. Assume that this travel time is distributed uniformly between 0 and 2
minutes. Modify your simulation and rerun it under the same conditions as in
part (a).