The physics of the Mt/G/ ∞ symbol Queue
Operations Research
Peak congestion in multi-server service systems with slowly varying arrival rates
Queueing Systems: Theory and Applications
Control and recovery from rare congestion events in a large multi-server system
Queueing Systems: Theory and Applications
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Many service systems have demand that varies significantly by time of day, making it costly to provide sufficient capacity to be able to respond very quickly to each service request. Fortunately, however, different service requests often have very different response-time requirements. Some service requests may need immediate response, while others can tolerate substantial delays. Thus it is often possible to smooth demand by partitioning the service requests into separate priority classes according to their response-time requirements. Classes with more stringent performance requirements are given higher priority for service. Lower capacity may be required if lower-priority-class demand can be met during off-peak periods. We show how the priority classes can be defined and the resulting required fixed capacity can be determined, directly accounting for the time-dependent behavior. For this purpose, we exploit relatively simple analytical models, in particular, M"t/G/~ and deterministic offered-load models. The analysis also provides an estimate of the capacity savings that can be obtained from partitioning time-varying demand into priority classes.