The number of overlapping customers

Onno Boxma

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

Abstract

We consider the number of overlapping customers in several single- and multiserver queues, i.e., the number of customers whose visit to a service system at some point in time has an overlap with that of a tagged customer. Restricting ourself to the FCFS policy, we obtain the probability generating function and moments of the number of overlaps in the M / G / 1 , M / G / 1 / N , M / M / c and G / M / c queue and (as an approximation) the M / G / c queue.

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References

1979Approximations of the Mean Waiting Time in an M/G/s Queueing System 20202020 Winter Simulation Conference (WSC)1995Stochastic Models: An Algorithmic Approach.2020Reducing risk of infection – The COVID-19 queueing game 2022A queueing‐theoretic framework for evaluating transmission risks in service facilities during a pandemic 1984Joint distribution of sojourn time and queue length in the M/G/1 queue with (in) finite capacity 2023Overlap times in the infinite server queue 2025Queueing management for reducing the overlaps of customers in service systems

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