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Customer requests for service arrive randomly at
one or more service groups. Each request is handled
by one of several servers in the group. The time
to handle the request is a random variable. If all
servers in the group are busy, then the request
waits until a server is free.
For each service group we know the mean arrival rate of requests, the mean service time, and the standard deviation in service time.
We are interested in how many servers, e.g., tech support people, to allocate to each service group, given a fixed number of servers available overall.
Because arrivals and service times are random, if we set capacity only slightly larger than incoming load, there may be intervals in which large queues develop, and so the average waiting time will be large. To reduce average waiting time we must increase capacity above the average arriving load. If arrivals are in a stationary Poisson process, and the service times have an exponential distribution, the so-called M/M/c case, then the calculated results are exact, else they are approximate.;