An Empirical Investigation of the Transient Behavior of Stationary Queueing Systems

Article Abstract:

The transient behavior of infinite-capacity, single-server, Markovian queueing systems is examined. It estimates Q(t), the expected number of customers in queue at time t, by numerically solving the sets of simultaneous, first-order differential equations that describe these systems. Empirical results have been drawn from these observations. For small values of t, the behavior of Q(t) is strongly influenced by the initial conditions. One can predict which of a small set of patterns this behavior will follow. After an initial period of time and independently of initial conditions, Q(t) approaches Q (infinity) in a manner that can be approximated through a decaying exponential function. On the basis of experimental evidence, we have developed an expression that provides a good approximation to the observed values of the time constant associated with this exponential function. Tables and graphs are included.

Systems, Markov Process

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A Queueing Model for Telephone Operator Staffing

Article Abstract:

The problem of telephone operator staffing is addressed. A queueing model is developed that reduces the cost of staffing while maintaining an acceptable service level. Workforce levels are derived from load forecasts. There are large server team sizes, bimodal service time distributions, nonstationary arrivals, customer abandonments and reattempts. Graphs and tables are used to illustrate results.

Telephone companies, Forecasting, Personnel, Applications, Models, Telephone Company, Queuing Networks, Simulations

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A Convexity Result for a Class of GI-G-1 Queueing Systems

Article Abstract:

It is helpful to know that a local extremum is a global extremum when designing stochastic systems. It is shown that the expected number of customers in any GI-G-1 FCFS queueing system is convex in the service rate. This is true if the arrival time of each customer is independent of the service rate and if the workload of each customer is independent of the service rate.

Stochastic Model

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