Example 1 Consider a queue where customers arrive one by one. There is a single server that serves each customer on a first-come-first-served basis. Define the sojourn time experienced by a customer as the time he/she spends in the system: waiting (if any) for service plus the duration of the service at the server. The server toggles between being idle for some time when there are no customers ...

In this paper we study the sample paths during a busy period of a Finite MEP/MEP/1 system, where both the arrivals and service processes can be serially auto-correlated Matrix Exponential Processes and provide a mechanism to compute the expected number of customers served during a finite queue’s busy period. We then show some numeric results by computing the probabilities of serving exactly n c...

This paper presents a sensitivity investigation of the expected busy period for a controllable M/G/1 queueing system by means of a factorial design statistical analysis. We studies the effect of four important factors (parameters) that influence the expected busy period of an M/G/1 system, in which the server operates -policy in his idle period. A 2 4 factorial experimental design is used ...

The error between the actual value of the mean busy periQ..d and the value estimaled by a common queueing tormula (D;:;: SOl (i-V)) is evaluated. tDenning's addre:'l!l: Department of Compu.ter Sciences, Purdue University, W. Lafayette, IN 41907 USA. KoweJk's addre:iS: FClchbcrcich Inrormatik, Univer:ritut Hamburg. RoUlerbllumschau9ce 07/09, 2000 Hamburg 10, West Gcrmuny.

The busy period for a queue is cast as the area swept under the random walk until it first returns to zero. Encompassing non-i.i.d. increments, the large-deviations asymptotics of the busy period B is addressed, under the assumption that the increments satisfy standard conditions, including a negative drift. The main conclusions provide insight on the probability of a large busy period, and the...

In this paper we find the waiting time distribution in the transient domain and the busy period distribution of the GI/G/I queue. We formulate the problem as a two-dimensional Lindley process and then transform it to a Hilbert factorization problem. We achieve the solution of the factorization problem for the GI/R/I, R/G/I queues, where R is the class of distributions with rational Laplace tran...

This paper analyzes a discrete-time $Geo/Geo/c$ queueing system with multiple working vacations and reneging in which customers arrive according to a geometric process. As soon as the system gets empty, the servers go to a working vacations all together. The service times during regular busy period, working vacation period and vacation times are assumed to be geometrically distributed. Customer...