Publisher Summary This chapter discusses the queueing theory. Queueing theory concerns
the construction and analysis of mathematical models of systems that provide service to …

This note illustrates that a combination of the approach in our previous papers (Boucherie
and Boxma, 1996, Probability in the Engineering and Informational Sciences10: 261–277; …

We study a generalization of the GI/G/l queue in which the server is turned off at the end of
each busy period and is reactivated only when the sum of the service times of all waiting …

Using constructive, sample-path arguments, we derive a variety of transform-free results
about queue lengths and waiting times for the M/G/1/K queue. In classical analyses of …

The classical renewal-theory (waiting-time, or inspection) paradox states that the length of
the renewal interval that covers a randomly-selected time epoch tends to be longer than an …

Consider the GI/GI/1 queue with the Last-Come First-Served Preemptive-Resume service
discipline. We give intuitive explanations for (1) the geometric nature of the stationary queue …

We generalize the classical ballot theorem and use it to obtain direct probabilistic
derivations of some well-known and some new results relating to busy and idle periods and …

We study in this paper an approximation method for the calculation of various performance
measures of a GI/G/1 queue. Instead of solving the waiting time directly, we analyze the idle …

Using a generalization of the classical ballot theorem, Niu and Cooper [7] established a
duality relation between the joint distribution of several variables associated with the busy …

A variety of performance measures of a GI/G/1 queue are explicitly related to the idle-period
distribution of the queue, suggesting that the system analysis can be accomplished by the …