Topic
M/D/1 queue
About: M/D/1 queue is a research topic. Over the lifetime, 2099 publications have been published within this topic receiving 40073 citations.
Papers published on a yearly basis
1 / 2
Papers
1 Jan 1991
TL;DR: This work generalizes results to the single server queue with the batch arrival process and emphasizes the resulting simplifications of the computational complexity of the algorithmic solution of single server queues with a general 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...
1,103 citations
TL;DR: The equilibrium joint probability distribution of queue lengths is obtained for a broad class of jobshop-like "networks of waiting lines," where the mean arrival rate of customers depends almost arbitrarily upon the number already present, and the mean service rate at each service center depends almost arbitrary upon the queue length there.
Abstract: (This article originally appeared in Management Science, November 1963, Volume 10, Number 1, pp. 131-142, published by The Institute of Management Sciences.)
The equilibrium joint probability distribution of queue lengths is obtained for a broad class of jobshop-like "networks of waiting lines," where the mean arrival rate of customers depends almost arbitrarily upon the number already present, and the mean service rate at each service center depends almost arbitrarily upon the queue length there. This extension of the author's earlier work is motivated by the observation that real production systems are usually subject to influences which make for increased stability by tending, as the amount of work-in-process grows, to reduce the rate at which new work is injected or to increase the rate at which processing takes place.
954 citations
IBM1
TL;DR: 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.
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. >
928 citations
TL;DR: 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.
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.
604 citations
TL;DR: The classical single server vacation model is generalized to consider a server which works at a different rate rather than completely stops during the vacation period, which approximates a multi-queue system whose service rate is one of the two speeds for which the fast speed mode cyclically moves from queue to queue with an exhaustive schedule.
474 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2019 | 1 |
| 2018 | 6 |
| 2017 | 33 |
| 2016 | 43 |
| 2015 | 69 |
| 2014 | 62 |