Numerical analysis for bulk-arrival queueing systems: Root-finding and steady-state probabilities inGI r /M/1 queues

1987 ◽  
Vol 8 (1) ◽  
pp. 307-320 ◽  
Author(s):  
M. L. Chaudhry ◽  
J. L. Jain ◽  
J. G. C. Templeton
Keyword(s):  
Steady State ◽  
Numerical Analysis ◽  
Queueing Systems ◽  
Root Finding ◽  
Bulk Arrival ◽  
Steady State Probabilities

A note on the waiting time in M[X]/G/1 queueing systems with a removable server

2004 ◽  
Vol 41 (1) ◽  
pp. 287-291
Author(s):  
Jacqueline Loris-Teghem
Keyword(s):  
Distribution Function ◽  
Steady State ◽  
Waiting Time ◽  
Queueing Systems ◽  
Stieltjes Transform ◽  
Steady State Distribution ◽  
State Distribution ◽  
Removable Server ◽  
Inactive Phase ◽  
Bulk Arrival

For the M[X]/G/1 queueing model with a general exhaustive-service vacation policy, it has been proved that the Laplace-Stieltjes transform (LST) of the steady-state distribution function of the waiting time of a customer arriving while the server is active is the product of the corresponding LST in the bulk arrival model with unremovable server and another LST. The expression given for the latter, however, is valid only under the assumption that the number of groups arriving in an inactive phase is independent of the sizes of the groups. We here give an expression which holds in the general case. For the N-policy case, we also give an expression for the LST of the steady-state distribution function of the waiting time of a customer arriving while the server is inactive.

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

scholarly journals On a bulk queueing system with impatient customers

1998 ◽  
Vol 3 (6) ◽  
pp. 539-554 ◽  
Author(s):  
Lotfi Tadj ◽  
Lakdere Benkherouf ◽  
Lakhdar Aggoun
Keyword(s):  
Steady State ◽  
Queue Length ◽  
Queueing System ◽  
Impatient Customers ◽  
Ergodicity Condition ◽  
Bulk Service ◽  
Bulk Arrival ◽  
Steady State Probabilities ◽  
System Characteristics

We consider a bulk arrival, bulk service queueing system. Customers are served in batches ofrunits if the queue length is not less thanr. Otherwise, the server delays the service until the number of units in the queue reaches or exceeds levelr. We assume that unserved customers may get impatient and leave the system. An ergodicity condition and steady-state probabilities are derived. Various system characteristics are also computed.

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.

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.

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.

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.

Sign in / Sign up

Export Citation Format

Share Document