Consecutive customer loss probabilities in M/G/1/n and GI/M(m)//n systems

Antonio  Pacheco; Helena  Ribeiro

1st International ICST Workshop on Tools for solving Structured Markov Chains

Research Article

Consecutive customer loss probabilities in M/G/1/n and GI/M(m)//n systems

Cite: BibTeX Plain Text

@INPROCEEDINGS{10.1145/1190366.1190374,
    author={Antonio  Pacheco and Helena  Ribeiro},
    title={Consecutive customer loss probabilities in M/G/1/n and GI/M(m)//n systems},
    proceedings={1st International ICST Workshop on Tools for solving Structured Markov Chains},
    publisher={ACM},
    proceedings_a={SMCTOOLS},
    year={2012},
    month={4},
    keywords={Busy period consecutive customer loss probability M/G/1- /n queue GI/M(m)//n queue recursions stochastic ordering.},
    doi={10.1145/1190366.1190374}
}

Antonio Pacheco
Helena Ribeiro
Year: 2012
Consecutive customer loss probabilities in M/G/1/n and GI/M(m)//n systems
SMCTOOLS
ACM
DOI: 10.1145/1190366.1190374

Antonio Pacheco¹^,*, Helena Ribeiro¹^,*

1: Instituto Superior Tecnico, Department of Mathematics and CEMAT, Lisboa, Portugal.

*Contact email: apacheco@math.ist.utl.pt, mhcr@estg.ipleiria.pt

Abstract

We address the probability that k or more consecutive customer losses take place during a busy period of a queue, the so called k-CCL probability. We derive efficient algorithms to compute k-CCL probabilities in M/G/1/n and GI/M(m)//n systems for busy periods starting with an arbitrary number of customers in the system that, essentially, reduce to solving either simple recursions or linear systems of equations.

Keywords: Busy period consecutive customer loss probability M/G/1- /n queue GI/M(m)//n queue recursions stochastic ordering.

Published: 2012-04-05
Publisher: ACM

: http://dx.doi.org/10.1145/1190366.1190374