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2 results

  • A Pollaczek–Khintchine formula for M/G/1 queues with disasters

  • Part of
  • Gautam Jain, Karl Sigman
  • Journal:
    Journal of Applied Probability / Volume 33 / Issue 4 / December 1996
    Published online by Cambridge University Press:
    14 July 2016, pp. 1191-1200
    Print publication:
    December 1996

  • A disaster occurs in a queue when a negative arrival causes all the work (and therefore customers) to leave the system instantaneously. Recent papers have addressed several issues pertaining to queueing networks with negative arrivals under the i.i.d. exponential service times assumption. Here we relax this assumption and derive a Pollaczek–Khintchine-like formula for M/G/1 queues with disasters by making use of the preemptive LIFO discipline. As a byproduct, the stationary distribution of the remaining service time process is obtained for queues operating under this discipline. Finally, as an application, we obtain the Laplace transform of the stationary remaining service time of the customer in service for unstable preemptive LIFO M/G/1 queues.