Abstract
Motivated by a capacity allocation problem within a finite planning period, we conduct a transient analysis of a single-server queue with Lévy input. From a cost minimization perspective, we investigate the error induced by using stationary congestion measures as opposed to time-dependent measures. Invoking recent results from fluctuation theory of Lévy processes, we derive a refined cost function, that accounts for transient effects. This leads to a corrected capacity allocation rule for the transient single-server queue. Extensive numerical experiments indicate that the cost reductions achieved by this correction can be significant.
Highlights
The issue of matching a service system’s capacity to stochastic demand induced by its clients arises in many practical settings
Motivated by the time-varying nature of queues in practical applications, we studied the impact that the transient phase has on traditional capacity allocation questions
By defining a cost minimization problem in which the objective function contains a correction accounting for the transient period, we identified the leading and secondorder behavior of the cost function as a function of the interval length T
Summary
The issue of matching a service system’s capacity to stochastic demand induced by its clients arises in many practical settings. The resources available to satisfy demand are scarce and expensive. This forces the manager to consider a tradeoff between the system efficiency and the quality of service perceived by its clients. We focus on this trade-off in the context of the M/G/1 queue, in which the variable amenable for optimization is the server speed μ. Optimizing the server speed μ in a single-server queue in a timehomogeneous environment, while trading off congestion levels against capacity allocation costs, does not pose any technical challenges. The objective function to be minimized, the total cost function, has the shape
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