Temps d’attente et nombre de clients dans une file D/D/1
The busy period of a repairman attending a unit parallel system
The busy period of a repairman for redundant repairable systems
The GI/G/1 model with warming-up time
The Intermittent Server
The , queue with preemptive priority.
The queue with queue length dependent service times.
The M/G/1 retrial queue: an information theoretic approach.
In this paper, we give a survey of the use of information theoretic techniques for the estimation of the main performance characteristics of the M/G/1 retrial queue. We focus on the limiting distribution of the system state, the length of a busy period and the waiting time. Numerical examples are given to illustrate the accuracy of the maximum entropy estimations when they are compared versus the classical solutions.
The M/M/1 queue is Bernoulli
The classical output theorem for the M/M/1 queue, due to Burke (1956), states that the departure process from a stationary M/M/1 queue, in equilibrium, has the same law as the arrivals process, that is, it is a Poisson process. We show that the associated measure-preserving transformation is metrically isomorphic to a two-sided Bernoulli shift. We also discuss some extensions of Burke's theorem where it remains an open problem to determine if, or under what conditions, the analogue of this result...
The Modified M/G/1 queue
The MX/M/1 queue with working breakdown
In this paper, we consider a batch arrival MX/M/1 queue model with working breakdown. The server may be subject to a service breakdown when it is busy, rather than completely stoping service, it will decrease its service rate. For this model, we analyze a two-dimensional Markov chain and give its quasi upper triangle transition probability matrix. Under the system stability condition, we derive the probability generating function (PGF) of the stationary queue length, and then obtain its stochastic...
The Optimal Control in Batch Arrival Queue With Server Vacations, Startup and Breakdowns
The PH/M/c queue with varying environment
The queue-length in GI/G/ queues.
The repairman problem [Book]
The single server queue and the storage model: large deviations and fixed points.
The single server queue with Erlang input and semi-Markov service times
The stationary G/G/ queue.
The stationary G/G/ queue with non-identical servers.
The stationary local sojourn time in single server tandem queues with renewal input.