scholarly journals Calculating steady-state probabilities of single-channel closed queueing systems using hyperexponential approximation

2020 ◽  
Vol 19 (1) ◽  
pp. 113-120
Author(s):  
Yuriy Zhernovyi ◽  
Bohdan Kopytko
Keyword(s):  
Steady State ◽  
Single Channel ◽  
Queueing Systems ◽  
Steady State Probabilities

M/G/1 queueing systems with returning customers

1989 ◽  
Vol 26 (01) ◽  
pp. 152-163 ◽  
Author(s):  
Betsy S. Greenberg
Keyword(s):  
Steady State ◽  
Laplace Transform ◽  
Single Channel ◽  
Queueing Systems ◽  
Service Distribution ◽  
Poisson Arrivals ◽  
General Service ◽  
Steady State Probabilities

Single-channel queues with Poisson arrivals, general service distributions, and no queue capacity are studied. A customer who finds the server busy either leaves the system for ever or may return to try again after an exponentially distributed time. Steady-state probabilities are approximated and bounded in two different ways. We characterize the service distribution by its Laplace transform, and use this characterization to determine the better method of approximation.

M/G/1 queueing systems with returning customers

1989 ◽  
Vol 26 (1) ◽  
pp. 152-163 ◽  
Author(s):  
Betsy S. Greenberg
Keyword(s):  
Steady State ◽  
Laplace Transform ◽  
Single Channel ◽  
Queueing Systems ◽  
Service Distribution ◽  
Poisson Arrivals ◽  
General Service ◽  
Steady State Probabilities

Single-channel queues with Poisson arrivals, general service distributions, and no queue capacity are studied. A customer who finds the server busy either leaves the system for ever or may return to try again after an exponentially distributed time. Steady-state probabilities are approximated and bounded in two different ways. We characterize the service distribution by its Laplace transform, and use this characterization to determine the better method of approximation.

COMPUTATION OF STEADY-STATE PROBABILITIES FOR RESOURCE-SHARING CALL-CENTER QUEUEING SYSTEMS

2001 ◽  
Vol 17 (2) ◽  
pp. 191-214 ◽  
Author(s):  
Denise M. Bevilacqua Masi ◽  
Martin J. Fischer ◽  
Carl M. Harris
Keyword(s):  
Steady State ◽  
Resource Sharing ◽  
Call Center ◽  
Queueing Systems ◽  
Steady State Probabilities

On a certain type of network of queues

1975 ◽  
Vol 12 (1) ◽  
pp. 195-200 ◽  
Author(s):  
K. C. Madan
Keyword(s):  
Steady State ◽  
Single Channel ◽  
Service Channel ◽  
Poisson Stream ◽  
Queue Lengths ◽  
Parallel Channels ◽  
Service Times ◽  
Steady State Probabilities

The paper studies a network of queues in which units arrive singly in a Poisson stream at a service channel S from which they branch out into k parallel channels S1, S2, …, Sk. After having been serviced at S1, S2, … Sk, the units converge again into a single channel S′. The service times of units at each of the channels are assumed to be exponential. Units finally serviced at S’ may leave the system or may again join S. This has been considered by taking two models denoted as Model A and Model B. Steady-state probabilities giving the number of units present in the system have been obtained explicitly for both the models. The expressions for mean queue lengths have also been arrived at.

scholarly journals Markov chains with quasitoeplitz transition matrix: applications

1990 ◽  
Vol 3 (2) ◽  
pp. 141-152
Author(s):  
A. M. Dukhovny
Keyword(s):  
Steady State ◽  
Markov Chains ◽  
Generating Functions ◽  
Transition Matrix ◽  
Queueing Systems ◽  
Warm Up ◽  
Hitting Probabilities ◽  
Steady State Probabilities ◽  
Transient And Steady State

Application problems are investigated for the Markov chains with quasitoeplitz transition matrix. Generating functions of transient and steady state probabilities, first zero hitting probabilities and mean times are found for various particular cases, corresponding to some known patterns of feedback ( “warm-up,” “switch at threshold” etc.), Level depending dams and queue-depending queueing systems of both M/G/1 and MI/G/1 types with arbitrary random sizes of arriving and departing groups are studied.

scholarly journals Markov chains with quasitoeplitz transition matrix

1989 ◽  
Vol 2 (1) ◽  
pp. 71-82 ◽  
Author(s):  
Alexander M. Dukhovny
Keyword(s):  
Steady State ◽  
Boundary Value Problem ◽  
Markov Chains ◽  
Generating Functions ◽  
Transition Matrix ◽  
Queueing Systems ◽  
Riemann Boundary Value Problem ◽  
Riemann Boundary ◽  
Steady State Probabilities ◽  
Transient And Steady State

This paper investigates a class of Markov chains which are frequently encountered in various applications (e.g. queueing systems, dams and inventories) with feedback. Generating functions of transient and steady state probabilities are found by solving a special Riemann boundary value problem on the unit circle. A criterion of ergodicity is established.

On a certain type of network of queues

1975 ◽  
Vol 12 (01) ◽  
pp. 195-200
Author(s):  
K. C. Madan
Keyword(s):  
Steady State ◽  
Single Channel ◽  
Service Channel ◽  
Poisson Stream ◽  
Queue Lengths ◽  
Parallel Channels ◽  
Service Times ◽  
Steady State Probabilities

The paper studies a network of queues in which units arrive singly in a Poisson stream at a service channel S from which they branch out into k parallel channels S 1 , S 2, …, Sk. After having been serviced at S 1, S 2, … Sk , the units converge again into a single channel S′. The service times of units at each of the channels are assumed to be exponential. Units finally serviced at S’ may leave the system or may again join S. This has been considered by taking two models denoted as Model A and Model B. Steady-state probabilities giving the number of units present in the system have been obtained explicitly for both the models. The expressions for mean queue lengths have also been arrived at.

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