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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

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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
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