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Blocking Probabilities in Mobile Communications Networks with Time-Varying Rates and Redialing Subscribers

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  • Nadra Abdalla
  • Richard Boucherie

Abstract

Call-blocking probabilities are among the key performance measures in mobile communications networks. For their analysis, mobile networks can be modelled as networks of Erlang loss queues with common capacity restrictions dictated by the allocation of frequencies to the cells of the network. However, due to the time-varying load offered to the cells of such networks, blocking probabilities usually cannot be obtained in closed form. The relation between networks of Erlang loss queues and networks of infinite server queues, for which the time-dependent occupancy distribution is multidimensional Poisson, suggests to use that distribution as approximate distribution for the network of Erlang loss queues. This paper extends this so-called Modified Offered Load (MOL) approximation to networks of Erlang loss queues, and also allows subscribers that find their call blocked to redial to continue their call. For GSM networks operating under Fixed Channel Allocation, it is shown that blocking probabilities are increasing in the redial rates so that the MOL approximation that is most accurate for maximal redial rates turns out to be fairly accurate for the resulting upper bound for blocking probabilities. The accuracy is explicitly evaluated in an application of the results towards blocking probabilities in a hot spot travelling along a road through a GSM network. Copyright Kluwer Academic Publishers 2002

Suggested Citation

  • Nadra Abdalla & Richard Boucherie, 2002. "Blocking Probabilities in Mobile Communications Networks with Time-Varying Rates and Redialing Subscribers," Annals of Operations Research, Springer, vol. 112(1), pages 15-34, April.
    • Handle: RePEc:spr:annopr:v:112:y:2002:i:1:p:15-34:10.1023/a:1020968702818
    DOI: 10.1023/A:1020968702818
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    Cited by:

    1. Yanting Chen & Jingui Xie & Taozeng Zhu, 2023. "Overflow in systems with two servers: the negative consequences," Flexible Services and Manufacturing Journal, Springer, vol. 35(3), pages 838-863, September.
    2. Xi Chen & Dave Worthington, 2017. "Staffing of time-varying queues using a geometric discrete time modelling approach," Annals of Operations Research, Springer, vol. 252(1), pages 63-84, May.
    3. Stef Baas & Sander Dijkstra & Aleida Braaksma & Plom Rooij & Fieke J. Snijders & Lars Tiemessen & Richard J. Boucherie, 2021. "Real-time forecasting of COVID-19 bed occupancy in wards and Intensive Care Units," Health Care Management Science, Springer, vol. 24(2), pages 402-419, June.
    4. Md Asaduzzaman & Thierry Chaussalet & Nicola Robertson, 2010. "A loss network model with overflow for capacity planning of a neonatal unit," Annals of Operations Research, Springer, vol. 178(1), pages 67-76, July.
    5. Izady, N. & Worthington, D., 2011. "Approximate analysis of non-stationary loss queues and networks of loss queues with general service time distributions," European Journal of Operational Research, Elsevier, vol. 213(3), pages 498-508, September.

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