Comments on: recent developments in the queueing problem
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The problem of queues and waiting times is part of our daily life and so it is a situation that deserves a thorough study. Queueing theory mathematically studies the waiting lines and is part of the operations research field. This problem involves more complexity since it considers: the arrival process of the agents (customers) according to some probability distribution; the service time distribution and the number of available servers (in line or in parallel); and, finally, the queue discipline that determines the method used to serve the agents: first come, first served; last come, first served; etc.
Chun presents a nice survey about the recent results on queueing problems where: there is only one server; the service time is the same for all agents (normalized to one); agents arrive according to some stochastic process; congestion may occur, and so the agents incur in waiting costs. The objective in this model, introduced by Dolan (1978), is to find an allocation rule that fixes the...