A Waiting Line with Interrupted Service, Including Priorities

摘要: SUMMARY A single-server system with stationary compound Poisson input and general independent service times, the latter being subject to random interruptions of independently but otherwise arbitrarily distributed durations, is studied. For a variety service-interruption interactions (including preemptiverepeat) distributions busy period duration, queue length, waiting time are characterized by transforms moments. Applications made priority scheduling problems. MANY situations in which lines develop occurrence customer service. Such may be caused breakdowns machine that provides service, for example, an electronic computer. Also, if certain customers assigned priority, then appearance one these bring about interruption servicing low-priority customers. In practice it would not surprising find systems experience both sorts. this paper we consider effect upon waiting-line process following kind: appear accordance (i.e. bunches arrive randomly), served turn single facility. The basic times independently, identically, arbitrarily, distributed. Interruptions at random, sense that, currently free interruption, until next occurs exponentially Interruption durations Without described has been discussed Gaver (1959); present adaptation approach needs problem. Previous treatments similar problems, emphasizing priorities, have given Cobham (1954), Stephan (1956), Kesten Runnenberg (1957), White Christie (1958), Morse (1958, Chapter 9) Miller (1960). influence behaviour cannot investigated without specifying detail interaction between process. Throughout will assumed all occurring during particular customer's must take during, or immediately after, period. Thus preemptive, summarily breaking progress, postponable end period, beyond. If preemptive possible resume from point took place when cleared; such (between interruption) called