Concepedia

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

Alexander Dudin, Shōichi Nishimura

Journal of Applied Probability · 1999 · 62 citations · 14 references

DOI

Concepts

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.

References

14

New results on the single server queue with a batch markovian arrival process

David M. Lucantoni · Communications in Statistics Stochastic Models · 1991 · 1.1K citations

, , +13

Structured Stochastic Matrices of M/G/1 Type and Their Applications.

B. W. Conolly, Marcel F. Neuts · Journal of the Royal Statistical Society Series C (Applied Statistics) · 1991 · 1K citations

, , +8

Product-form queueing networks with negative and positive customers

Erol Gelenbe · Journal of Applied Probability · 1991 · 510 citations

, , +12

Spectral analysis of<i>M/G/</i>1 and<i>G</i>/<i>M</i>/1 type Markov chains

H. Richard Gail, S. L. Hantler, B. A. Taylor · Advances in Applied Probability · 1996 · 179 citations

, , +16

A Pollaczek–Khintchine formula for<i>M</i>/<i>G</i>/1 queues with disasters

Gautam Jain, Karl Sigman · Journal of Applied Probability · 1996 · 130 citations

, , +16