Topic
M/M/∞ queue
About: M/M/∞ queue is a research topic. Over the lifetime, 1499 publications have been published within this topic receiving 29001 citations.
Papers published on a yearly basis
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Papers
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
TL;DR: This paper analyzes the simplest abandonment model, in which customers' patience is exponentially distributed and the system's waiting capacity is unlimited ( M/ M/ N +M), and derives approximations for performance measures and proposes "rules of thumb" for the design of large call centers.
Abstract: The most common model to support workforce management of telephone call centers is theM/ M/ N/ B model, in particular its special casesM/ M/ N (Erlang C, which models out busy signals) andM/ M/ N/ N (Erlang B, disallowing waiting). All of these models lack a central prevalent feature, namely, that impatient customers might decide to leave (abandon) before their service begins.In this paper, we analyze the simplest abandonment model, in which customers' patience is exponentially distributed and the system's waiting capacity is unlimited ( M/ M/ N +M). Such a model is both rich and analyzable enough to provide information that is practically important for call-center managers. We first outline a method for exact analysis of theM/ M/ N +M model, that while numerically tractable is not very insightful. We then proceed with an asymptotic analysis of theM/ M/ N +M model, in a regime that is appropriate for large call centers (many agents, high efficiency, high service level). Guided by the asymptotic behavior, we derive approximations for performance measures and propose "rules of thumb" for the design of large call centers. We thus add support to the growing acknowledgment that insights from diffusion approximations are directly applicable to management practice.
676 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
TL;DR: A single-server queueing system with constant Poisson input is considered and the partial elimination of the service station's idle fraction is envisaged by intermittent close-down and set-up.
Abstract: A single-server queueing system with constant Poisson input is considered and the partial elimination of the station's idle fraction is envisaged by intermittent close-down and set-up. The rule pertaining to the dismantling and re-establishing of the service station—the management doctrine—is based on the instantaneous size of the queue, but these processes are assumed to consume time. Operating characteristics of such systems—in particular, average queue length and queueing time—are evaluated. A cost structure is superimposed on the system and optimization procedures are outlined. The close relationship with (a) priority queueing and (b) storage models is pointed out.
465 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 1 |
| 2020 | 2 |
| 2019 | 3 |
| 2018 | 9 |
| 2017 | 21 |
| 2016 | 40 |