A max-algebra approach to modeling and simulation of tandem queueing systems

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A max-algebra approach to modeling and simulation of tandem queueing systems. / Krivulin, N. K.

In: Mathematical and Computer Modelling, Vol. 22, No. 3, 08.1995, p. 25-37.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{3fe4bc607a904cfb8f1f88ecd18d5a0b,

title = "A max-algebra approach to modeling and simulation of tandem queueing systems",

abstract = "Max-algebra models of tandem single-server queueing systems with both finite and infinite buffers are developed. The dynamics of each system is described by a linear vector state equation similar to those in the conventional linear systems theory, and it is determined by a transition matrix inherent in the system. The departure epochs of a customer from the queues are considered as state variables, whereas its service times are assumed to be system parameters. We show how transition matrices may be calculated from the service times, and present the matrices associated with particular models. We also give a representation of system performance measures including the system time and the waiting time of customers, associated with the models. As an application, both serial and parallel simulation procedures are presented, and their performance is outlined.",

keywords = "max-algebra, tandem queues, dynamic state equation, performance measure, parallel simulation algorithm",

author = "Krivulin, {N. K.}",

year = "1995",

month = aug,

doi = "10.1016/0895-7177(95)00117-K",

language = "English",

volume = "22",

pages = "25--37",

journal = "Mathematical and Computer Modelling",

issn = "0895-7177",

publisher = "Elsevier",

number = "3",

}

RIS

TY - JOUR

T1 - A max-algebra approach to modeling and simulation of tandem queueing systems

AU - Krivulin, N. K.

PY - 1995/8

Y1 - 1995/8

N2 - Max-algebra models of tandem single-server queueing systems with both finite and infinite buffers are developed. The dynamics of each system is described by a linear vector state equation similar to those in the conventional linear systems theory, and it is determined by a transition matrix inherent in the system. The departure epochs of a customer from the queues are considered as state variables, whereas its service times are assumed to be system parameters. We show how transition matrices may be calculated from the service times, and present the matrices associated with particular models. We also give a representation of system performance measures including the system time and the waiting time of customers, associated with the models. As an application, both serial and parallel simulation procedures are presented, and their performance is outlined.

AB - Max-algebra models of tandem single-server queueing systems with both finite and infinite buffers are developed. The dynamics of each system is described by a linear vector state equation similar to those in the conventional linear systems theory, and it is determined by a transition matrix inherent in the system. The departure epochs of a customer from the queues are considered as state variables, whereas its service times are assumed to be system parameters. We show how transition matrices may be calculated from the service times, and present the matrices associated with particular models. We also give a representation of system performance measures including the system time and the waiting time of customers, associated with the models. As an application, both serial and parallel simulation procedures are presented, and their performance is outlined.

KW - max-algebra

KW - tandem queues

KW - dynamic state equation

KW - performance measure

KW - parallel simulation algorithm

U2 - 10.1016/0895-7177(95)00117-K

DO - 10.1016/0895-7177(95)00117-K

M3 - Article

VL - 22

SP - 25

EP - 37

JO - Mathematical and Computer Modelling

JF - Mathematical and Computer Modelling

SN - 0895-7177

IS - 3

ER -

ID: 5037761