A Multi-server Queueing System with Backup Servers

2018 ◽  
pp. 117-128
Author(s):  
Valentina Klimenok ◽  
Alexander Dudin ◽  
Uladzimir Shumchenia
Keyword(s):  
Queueing System ◽  
Multi Server

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.

Stochastic Control Optimization Technique on Multi-Server Markovian Queueing System

2011 ◽  
Vol 3 (7) ◽  
pp. 375-378
Author(s):  
K. Sivaselvan K. Sivaselvan ◽  
◽  
C. Vijayalakshmi C. Vijayalakshmi
Keyword(s):  
Stochastic Control ◽  
Queueing System ◽  
Optimization Technique ◽  
Control Optimization ◽  
Multi Server

The steady state of a multi-server mixed queue

1973 ◽  
Vol 5 (03) ◽  
pp. 614-631 ◽  
Author(s):  
N. B. Slater ◽  
T. C. T. Kotiah
Keyword(s):  
Steady State ◽  
Statistical Mechanics ◽  
Generating Functions ◽  
Queueing System ◽  
Linear Equations ◽  
Weighted Sum ◽  
System Of Linear Equations ◽  
Different Types ◽  
Multi Server ◽  
Steady State Probabilities

In a multi-server queueing system in which the customers are of several different types, it is useful to define states which specify the types of customers being served as well as the total number present. Analogies with some problems in statistical mechanics are found fruitful. Certain generating functions are defined in such a way that they satisfy a system of linear equations. Solution of the associated eigenvector problem shows that the steady-state probabilities for states in which all the servers are busy can be represented by a weighted sum of geometric probabilities.

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