M/G/c/K PERFORMANCE MODELS IN MANUFACTURING AND SERVICE SYSTEMS

2008 ◽  
Vol 25 (04) ◽  
pp. 531-561 ◽  
Author(s):  
J. MACGREGOR SMITH
Keyword(s):  
Performance Measures ◽  
Queueing Systems ◽  
Service Systems ◽  
Finite Buffer ◽  
Performance Models ◽  
Performance Modelling ◽  
Server Systems ◽  
Approximation Formulas ◽  
Intractable Problem ◽  
Multi Server

Multi-server, finite buffer, performance models of queueing systems are very useful tools for manufacturing, telecommunication, transportation and facility modelling applications. Exact computation of performance measures for general service multi-server queueing systems remains an intractable problem. Approximations of these performance measures are important to quickly and accurately reveal the performance of a system. This is desirable for both performance evaluation as well as optimization of these systems. Two-moment approximation formulas are presented for performance modelling of multi-server systems involving servers of 2,3,…,10 servers. Extensive computational results are provided to evaluate the approximation results against simulation, known tabular results, and other approximation formulas. Applications of the model to optimizing manufacturing and service systems using a marginal allocation algorithm are briefly illustrated. Extensions of the two-moment methodology to larger multi-server systems c = {25, 50, 100} round out the paper.

Optimal design of a multi-server queueing system with delay information

2016 ◽  
Vol 116 (1) ◽  
pp. 147-169 ◽  
Author(s):  
Miao Yu ◽  
Jun Gong ◽  
Jiafu TANG
Keyword(s):  
Optimal Design ◽  
Performance Measures ◽  
Call Center ◽  
Queueing System ◽  
Call Centers ◽  
Queueing Systems ◽  
Staffing Level ◽  
Content Type ◽  
Multi Server ◽  
Delay Information

Purpose – The purpose of this paper is to provide a framework for the optimal design of queueing systems of call centers with delay information. The main decisions in the design of such systems are the number of servers, the appropriate control to announce delay anticipated. Design/methodology/approach – This paper models a multi-server queueing system as an M/M/S+M queue with customer reactions. Based on customer psychology in waiting experiences, a number of different service-level definitions are structured and the explicit computation of their performance measures is performed. This paper characterizes the level of satisfaction with delay information to modulate customer reactions. Optimality is defined as the number of agents that maximize revenues net of staffing costs. Findings – Numerical studies show that the solutions to optimal design of staffing levels and delay information exhibit interesting differences, especially U-shaped curve for optimal staffing level. Experiments show how call center managers can determine economically optimal anticipated delay and number of servers so that they could control the trade-off between revenue loss and customer satisfaction. Originality/value – Many results that pertain to announcing delay information, customer reactions, and links to satisfaction with delay information have not been established in previous studies, however, this paper analytically characterizes these performance measures for staffing call centers.

scholarly journals A Taylor Series Approach for Service-Coupled Queueing Systems with Intermediate Load

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Ekaterina Evdokimova ◽  
Sabine Wittevrongel ◽  
Dieter Fiems
Keyword(s):  
Performance Measures ◽  
Queueing Systems ◽  
Poisson Processes ◽  
Series Expansions ◽  
Service Rate ◽  
Single Server ◽  
Queueing Model ◽  
State Space Explosion ◽  
Finite Queues ◽  
Service Rates

This paper investigates the performance of a queueing model with multiple finite queues and a single server. Departures from the queues are synchronised or coupled which means that a service completion leads to a departure in every queue and that service is temporarily interrupted whenever any of the queues is empty. We focus on the numerical analysis of this queueing model in a Markovian setting: the arrivals in the different queues constitute Poisson processes and the service times are exponentially distributed. Taking into account the state space explosion problem associated with multidimensional Markov processes, we calculate the terms in the series expansion in the service rate of the stationary distribution of the Markov chain as well as various performance measures when the system is (i) overloaded and (ii) under intermediate load. Our numerical results reveal that, by calculating the series expansions of performance measures around a few service rates, we get accurate estimates of various performance measures once the load is above 40% to 50%.

scholarly journals Zero Queueing for Multi-Server Jobs

2021 ◽  
Vol 5 (1) ◽  
pp. 1-25
Author(s):  
Weina Wang ◽  
Qiaomin Xie ◽  
Mor Harchol-Balter
Keyword(s):  
Cloud Computing ◽  
Stability Region ◽  
Transient Analysis ◽  
Queueing Systems ◽  
Sufficient Conditions ◽  
Hard Problem ◽  
Queueing Model ◽  
Multiple Servers ◽  
First Results ◽  
Multi Server

Cloud computing today is dominated by multi-server jobs. These are jobs that request multiple servers simultaneously and hold onto all of these servers for the duration of the job. Multi-server jobs add a lot of complexity to the traditional one-server-per-job model: an arrival might not "fit'' into the available servers and might have to queue, blocking later arrivals and leaving servers idle. From a queueing perspective, almost nothing is understood about multi-server job queueing systems; even understanding the exact stability region is a very hard problem. In this paper, we investigate a multi-server job queueing model under scaling regimes where the number of servers in the system grows. Specifically, we consider a system with multiple classes of jobs, where jobs from different classes can request different numbers of servers and have different service time distributions, and jobs are served in first-come-first-served order. The multi-server job model opens up new scaling regimes where both the number of servers that a job needs and the system load scale with the total number of servers. Within these scaling regimes, we derive the first results on stability, queueing probability, and the transient analysis of the number of jobs in the system for each class. In particular we derive sufficient conditions for zero queueing. Our analysis introduces a novel way of extracting information from the Lyapunov drift, which can be applicable to a broader scope of problems in queueing systems.

Impact of Behavioral Factors on Performance of Multi-Server Queueing Systems

2017 ◽  
Author(s):  
Hung Do ◽  
Masha Shunko ◽  
Marilyn T. Lucas ◽  
David A. Novak
Keyword(s):  
Queueing Systems ◽  
Behavioral Factors ◽  
Multi Server

scholarly journals Considerations on Axial Compressor Bleed for Sub-Idle Performance Models

2020 ◽  
Author(s):  
Ferran Roig Tió ◽  
Luis E. Ferrer-Vidal ◽  
Hasani Azamar Aguirre ◽  
Vassilios Pachidis
Keyword(s):  
Flow Analysis ◽  
Axial Compressor ◽  
Engine Performance ◽  
Analysis Tool ◽  
Performance Models ◽  
Performance Modelling ◽  
Start Up ◽  
Considerable Impact ◽  
Aero Engines ◽  
Analytical Approaches

Abstract The trend towards increased bypass ratio and reduced core size in civil aero-engines puts a strain on ground-start and relight capability, prompting renewed interest in sub-idle performance modelling. While a number of studies have looked at some of the broad performance modelling issues prevalent in this regime, the effects that bleed can have on sub-idle performance have not been addressed in the literature. During start-up and relight, the unknown variation in bleed flows through open handling bleed valves can have a considerable impact on the compressor’s operating line. This paper combines experimental, numerical and analytical approaches to look at the effect that sub-idle bleed flows have on predicted start-up operating lines, along with their effect on compressor characteristics. Experimental whole-engine data along with a purpose-built core-flow analysis tool are used to assess the effect of bleed model uncertainty on engine performance models. An experimental rig is used to assess the effects of reverse bleed on compressor characteristics and measurements are compared against numerical results. Several strategies for the generation of sub-idle maps including bleed effects are investigated.

THE ALLOCATION OF CUSTOMERS IN A DISCRETE-TIME MULTI-SERVER QUEUEING SYSTEM

2010 ◽  
Vol 27 (06) ◽  
pp. 649-667 ◽  
Author(s):  
WEI SUN ◽  
NAISHUO TIAN ◽  
SHIYONG LI
Keyword(s):  
Performance Measures ◽  
Discrete Time ◽  
Queueing System ◽  
Arrival Rate ◽  
Allocation Problem ◽  
Optimal Outcome ◽  
The Subject ◽  
Multi Server ◽  
Theoretical Results

This paper, analyzes the allocation problem of customers in a discrete-time multi-server queueing system and considers two criteria for routing customers' selections: equilibrium and social optimization. As far as we know, there is no literature concerning the discrete-time multi-server models on the subject of equilibrium behaviors of customers and servers. Comparing the results of customers' distribution at the servers under the two criteria, we show that the servers used in equilibrium are no more than those used in the socially optimal outcome, that is, the individual's decision deviates from the socially preferred one. Furthermore, we also clearly show the mutative trend of several important performance measures for various values of arrival rate numerically to verify the theoretical results.

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