Queues with negative arrivals

Erol Gelenbe A · Peter W. Glynn · Karl Sigman

32 citations0/0 files storedJournal of Applied Probability

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Advanced Queuing Theory Analysis Probability and Risk Models Age of Information Optimization

Abstract

We study single-server queueing models where in addition to regular arriving customers, there are negative arrivals. A negative arrival has the effect of removing a customer from the queue. The way in which this removal is specified gives rise to several different models. Unlike the standard FIFO GI/GI/1 model, the stability conditions for these new models may depend upon more than just the arrival and service rates; the entire distributions of interarrival and service times may be involved.

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1988Queues as Harris recurrent Markov chains

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2004Markovian bulk-arriving queues with state-dependent control at idle time 1994State-dependent signalling in queueing networks 2017MX/M/c Queue with catastrophes and state-dependent control at idle time

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