34 research outputs found
Queueing Systems with Service Interruptions: An Approximation Model
International audienc
Simple bounds for queueing systems with breakdowns
Computationally attractive and intuitively obvious simple bounds are proposed for finite service systems which are subject to random breakdowns. The services are assumed to be exponential. The up and down periods are allowed to be generally distributed. The bounds are based on product-form modifications and depend only on means. A formal proof is presented. This proof is of interest in itself. Numerical support indicates a potential usefulness for quick engineering and performance evaluation purposes
Analysis of the finite-source multiclass priority queue with an unreliable server and setup time
In this article, we study a queueing system serving multiple classes of customers. Each class has a finite-calling population. The customers are served according to the preemptive-resume priority policy. We assume general distributions for the service times. For each priority class, we derive the steady-state system size distributions at departure/arrival and arbitrary time epochs. We introduce the residual augmented process completion times conditioned on the number of customers in the system to obtain the system time distribution. We then extend the model by assuming that the server is subject to operation-independent failures upon which a repair process with random duration starts immediately. We also demonstrate how setup times, which may be required before resuming interrupted service or picking up a new customer, can be incorporated in the model
The impact of disruption characteristics on the performance of a server
In this paper, we study a queueing system serving N customers with an unreliable server subject to disruptions even when idle. Times between server interruptions, service times, and times between customer arrivals are assumed to follow exponential distributions. The main contribution of the paper is to use general distributions for the length of server interruption periods/down
times. Our numerical analysis reveals the importance of incorporating the down time distribution into the model, since their impact on customer service levels could be counterintuitive. For instance, while higher down time variability increases the mean queue length, for other service levels, can prove to be improving system performance. We also show how the process completion time
approach from the literature can be extended to analyze the queueing system if the unreliable server fails only when it is serving a customer
Minimization of the blocking time of the unreliable Geo/G_D/1 queueing system
In this paper we study the blocking time of an unreliable single-server
queueing system . The service can be interrupted upon
explicit or implicit breakdowns. For the successful finish of the
service we use a special service discipline
dividing the pure service time (assumed to be a random variable
with known distribution) in subintervals with deterministically
selected time-points and making a copy at the end of each subinterval (if no
breakdowns occur during it) we derive the probability generating function of the blocking time of the server by a customer. As an application, we consider an unreliable system Geo/D/1 and the results is that the expected blocking time is minimized when the time-points t_0,t_1,... are equidistant. We determine the optimal number of copies and the length of the corresponding interval between two consecutive copies
The preemptive repeat hybrid server interruption model
We analyze a discrete-time queueing system with server interruptions and a hybrid preemptive repeat interruption discipline. Such a discipline encapsulates both the preemptive repeat identical and the preemptive repeat different disciplines. By the introduction and analysis of so-called service completion times, we significantly reduce the complexity of the analysis. Our results include a.o. the probability generating functions and moments of queue content and delay. Finally, by means of some numerical examples, we assess how performance measures are affected by the specifics of the interruption discipline