Basic Queueing - Formulation Previous Next
Before simulation can be applied to the Littletown bank problem, more information needs to be obtained about the anticipated pattern of interarrival times (the time between consecutive arrivals of customers into the bank) and of service times (the time required by a teller to serve a customer). Specifically, an estimate needs to be made of the probability distribution for each of these two kinds of times.
Remember that the minimum interarrival time is 0.5 minute (because the parking validation process takes at least 0.5 minute). The amount by which the interarrival time exceeds 0.5 minute is estimated to have an exponential distribution with a mean of 0.5 minute. Therefore, the total interarrival time has a translated exponential distribution with a mean of (0.5 + 0.5) = 1.0 minute. (A translated exponential distribution is just an exponential distribution with a constant added.)
Experience in other branch offices indicates that service time has approximately an Erlang distribution with a mean of 1.5 minutes and a shape parameter of  ( is required to be a positive integer), so that