M/G/k queue

About: M/G/k queue is a research topic. Over the lifetime, 3042 publications have been published within this topic receiving 54754 citations.

New results on the single server queue with a batch markovian arrival process

Abstract: The versatile Markovian point process was introduced by M. F. Neuts in 1979. This is a rich class of point processes whichcontains many familiar arrival process as very special cases. Recently, the Batch Markovian Arrival Process, a class of point processes which was subsequently shown to be equivalent to Neuts’ point process, has been studied using a more transparent notation. Recent results in the matrix-analytic approach to queueing theory have substantially reduced the computational complexity of the algorithmic solution of single server queues with a general Markovian arrival process. We generalize these results to the single server queue with the batch arrival process and emphasize the resulting simplifications. Algorithms for the special cases of the PH/G/l and MMPP/G/1 queues are highlighted as these models are receiving renewed attention in the literature and the new algorithms proposed here are simpler than existing ones. In particular, the PH/G/1 queue has additional structure which further enh...

Stability, queue length, and delay of deterministic and stochastic queueing networks

Abstract: We present two types of stability problems: 1) conditions for queueing networks that render bounded queue lengths and bounded delay for customers, and 2) conditions for queueing networks in which the queue length distribution of a queue has an exponential tail with rate /spl theta/. To answer these two types of stability problems, we introduce two new notions of traffic characterization: minimum envelope rate (MER) and MER with respect to /spl theta/. We also develop a set of rules for network operations such as superposition, input-output relation of a single queue, and routing. Specifically, we show that: 1) the MER of a superposition process is less than or equal to the sum of the MER of each process, 2) a queue is stable in the sense of bounded queue length if the MER of the input traffic is smaller than the capacity, 3) the MER of a departure process from a stable queue is less than or equal to that of the input process, and 4) the MER of a routed process from a departure process is less than or equal to the MER of the departure process multiplied by the MER of the routing process. Similar results hold for MER with respect to /spl theta/ under a further assumption of independence. For single class networks with nonfeedforward routing, we provide a new method to show that similar stability results hold for such networks under the first come, first served policy. Moreover, when restricting to the family of two-state Markov modulated arrival processes, the notion of MER with respect to /spl theta/ is shown to be equivalent to the recently developed notion of effective bandwidth in communication networks. >

Stochastic Decompositions in the M/G/1 Queue with Generalized Vacations

Abstract: This paper considers a class of M/G/1 queueing models with a server who is unavailable for occasional intervals of time. As has been noted by other researchers, for several specific models of this type, the stationary number of customers present in the system at a random point in time is distributed as the sum of two or more independent random variables, one of which is the stationary number of customers present in the standard M/G/1 queue i.e., the server is always available at a random point in time. In this paper we demonstrate that this type of decomposition holds, in fact, for a very general class of M/G/1 queueing models. The arguments employed are both direct and intuitive. In the course of this work, moreover, we obtain two new results that can lead to remarkable simplifications when solving complex M/G/1 queueing models.

Optimal incentive-compatible priority pricing for the M/M/1 queue

Abstract: Consider a system that is modeled as an M/M/1 queueing system with multiple user classes. Each class is characterized by its delay cost per unit of time, its expected service time and its demand function. This paper derives a pricing mechanism which is optimal and incentive-compatible in the sense that the arrival rates and execution priorities jointly maximize the expected net value of the system while being determined, on a decentralized basis, by individual users. A closed-form expression for the resulting price structure is presented and studied.

Utilization of Idle Time in an M/G/1 Queueing System

Abstract: This paper studies an M/G/1 queue where the idle time of the server is utilized for additional work in a secondary system. As usual, the server is busy as long as there are units in the main system...