A BMAP/SM/1 queueing system with Markovian arrival input of disasters

Alexander N. Dudin · Shōichi Nishimura

58 citations0/0 files storedJournal of Applied Probability

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Advanced Queuing Theory Analysis Probability and Statistical Research Probability and Risk Models

Abstract

Disaster arrival in a queuing system with negative arrivals causes all customers to leave the system instantaneously. Here we obtain a queue-length and virtual waiting (sojourn) time distribution for the more complicated system BMAP/SM/1 with MAP input of disasters.

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References

1991New results on the single server queue with a batch markovian arrival process 1991Structured Stochastic Matrices of M/G/1 Type and Their Applications.1991Product-form queueing networks with negative and positive customers 1996Spectral analysis ofM/G/1 andG/M/1 type Markov chains 1996A Pollaczek–Khintchine formula forM/G/1 queues with disasters 1994Some steady-state distributions for theMAP /SM /1 queue 1996The M/G/1 queue with negative customers 1997TheM/M/1 queue with mass exodus and mass arrivals when empty

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2001BMAP/SM/1 queue with Markovian input of disasters and non-instantaneous recovery 2004A MAP/G/1 Queue with Negative Customers 2010Bibliography on G-networks, negative customers and applications 2009A disaster queue with Markovian arrivals and impatient customers 2012Perturbation Bounds forMt/Mt/NQueue with Catastrophes 2010Markovian bulk-arrival and bulk-service queues with state-dependent control

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