A MATHEMATICAL PROGRAMMING APPROACH TO FUZZY TANDEM QUEUES

2005 ◽  
Vol 13 (04) ◽  
pp. 425-436 ◽  
Author(s):  
SHIH-PIN CHEN
Keyword(s):  
Performance Measures ◽  
Queueing Systems ◽  
Arrival Rate ◽  
Programming Approach ◽  
Extension Principle ◽  
Queueing Models ◽  
Membership Functions ◽  
Tandem Queues ◽  
Mathematical Programs ◽  
Mathematical Programming Approach

Tandem queueing models play an important role in many real world systems such as computer systems, production lines, and service systems. This paper proposes a procedure to construct the membership functions of the performance measures in tandem queueing systems, in that the arrival rate and service rates are fuzzy numbers. The basic idea is to transform a fuzzy tandem queue to a family of crisp tandem queues by applying the α -cut approach. Then on the basis of α -cut representation and the extension principle, a pair of mathematical programs is formulated to describe this family of crisp tandem queues, via which the membership functions of the performance measures are derived. Two numerical examples are solved successfully to demonstrate the validity of the proposed approach. Since the performance measures are expressed by membership functions rather than by crisp values, the fuzziness of input information is completely conserved. Thus the proposed approach for fuzzy systems can represent the system more accurately, and more information is provided for designing queueing systems. The successful extension of tandem queues to fuzzy environments permits tandem queueing models to have wider applications.

A note on the convexity of performance measures of M/M/c queueing systems

1983 ◽  
Vol 20 (04) ◽  
pp. 920-923 ◽  
Author(s):  
Hau Leung Lee ◽  
Morris A. Cohen
Keyword(s):  
Performance Measures ◽  
Waiting Time ◽  
Queueing System ◽  
Queueing Systems ◽  
Arrival Rate ◽  
Control Problems ◽  
Traffic Intensity ◽  
Expected Number ◽  
Expected Waiting Time

Convexity of performance measures of queueing systems is important in solving control problems of multi-facility systems. This note proves that performance measures such as the expected waiting time, expected number in queue, and the Erlang delay formula are convex with respect to the arrival rate or the traffic intensity of the M/M/c queueing system.

The impact of the composition of the customer base in general queueing models

1987 ◽  
Vol 24 (3) ◽  
pp. 709-724 ◽  
Author(s):  
A. Federgruen ◽  
H. Groenevelt
Keyword(s):  
Performance Measures ◽  
Arrival Rate ◽  
Queueing Models ◽  
Customer Base ◽  
New Class ◽  
Marginal Increase ◽  
The Impact

We consider general queueing models dealing with multiple classes of customers and address the question under what conditions and in what (stochastic) sense the marginal increase in various performance measures, resulting from the addition of a new class of customers to an existing system, is larger than if the same class were added to a system dealing with only a subset of its current customer base.Our results enhance our understanding of the dependence of various performance measures with respect to the composition of the customer base. In addition they translate readily into convexity results in an (appropriately defined) arrival rate.

scholarly journals Research on Fuzzy Three Stage Tandem Queues

2019 ◽  
Vol 8 (6S4) ◽  
pp. 1478-1481
Keyword(s):  
Membership Function ◽  
Performance Measures ◽  
Service Time ◽  
System Performance ◽  
Arrival Time ◽  
General Procedure ◽  
Membership Functions ◽  
Tandem Queues ◽  
The Membership Function

This project intends a general procedure to obtain the membership function of the performance measures in three stage tandem queues when the inter-arrival time and service time are in fuzzy. The basic idea is to diminish the crisp queue into fuzzy by applying the α-cut approach technique. A pair of parametric program is formulated to depict that family of crisp queue in which the membership functions of the system performance are acquired.

A note on the convexity of performance measures of M/M/c queueing systems

1983 ◽  
Vol 20 (4) ◽  
pp. 920-923 ◽  
Author(s):  
Hau Leung Lee ◽  
Morris A. Cohen
Keyword(s):  
Performance Measures ◽  
Waiting Time ◽  
Queueing System ◽  
Queueing Systems ◽  
Arrival Rate ◽  
Control Problems ◽  
Traffic Intensity ◽  
Expected Number ◽  
Expected Waiting Time

Convexity of performance measures of queueing systems is important in solving control problems of multi-facility systems. This note proves that performance measures such as the expected waiting time, expected number in queue, and the Erlang delay formula are convex with respect to the arrival rate or the traffic intensity of the M/M/c queueing system.

scholarly journals A Nonlinear Programming Approach for a Fuzzy Queue with an Unreliable Server

2012 ◽  
Vol 2 ◽  
pp. 44-56
Author(s):  
V. Ashok Kumar
Keyword(s):  
Fuzzy Numbers ◽  
Arrival Rate ◽  
Programming Approach ◽  
Service Rate ◽  
Membership Functions ◽  
Repair Rate ◽  
Breakdown Rate ◽  
Unreliable Server ◽  
The Family ◽  
System Characteristics

The aim of this paper is to develop the membership functions of the system characteristic of a queuing g model with an unreliable server, in which the arrival rate, service rate, breakdown rate and repair rate are all fuzzy numbers. The α-cut approach is used to transform a fuzzy queue with an unreliable server into a family of conventional crisp queues with an unreliable server. By using membership functions, a set of parametric nonlinear programmes are developed to describe the family of crisp queues with an unreliable server. An efficient algorithm is developed to find the optimal solutions at or different possibility level α. Numerical examples are solved successfully. Since the system characteristics being expressed and governed by membership functions, more information is provided for the management.

The impact of the composition of the customer base in general queueing models

1987 ◽  
Vol 24 (03) ◽  
pp. 709-724 ◽  
Author(s):  
A. Federgruen ◽  
H. Groenevelt
Keyword(s):  
Performance Measures ◽  
Arrival Rate ◽  
Queueing Models ◽  
Customer Base ◽  
New Class ◽  
Marginal Increase ◽  
The Impact

We consider general queueing models dealing with multiple classes of customers and address the question under what conditions and in what (stochastic) sense the marginal increase in various performance measures, resulting from the addition of a new class of customers to an existing system, is larger than if the same class were added to a system dealing with only a subset of its current customer base. Our results enhance our understanding of the dependence of various performance measures with respect to the composition of the customer base. In addition they translate readily into convexity results in an (appropriately defined) arrival rate.

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%.

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