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.

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.

On a decomposition result for a class of vacation queueing systems

1990 ◽  
Vol 27 (1) ◽  
pp. 227-231 ◽  
Author(s):  
Jacqueline Loris-Teghem
Keyword(s):  
Steady State ◽  
Time Distribution ◽  
Queueing Systems ◽  
Single Server ◽  
Service Time Distribution ◽  
Steady State Distribution ◽  
State Distribution ◽  
Random Size ◽  
Poisson Arrivals ◽  
General Service

We consider a single-server infinite-capacity queueing sysem with Poisson arrivals of customer groups of random size and a general service time distribution, the server of which applies a general exhaustive service vacation policy. We are concerned with the steady-state distribution of the actual waiting time of a customer arriving while the server is active.

Approximations for the steady-state probabilities in the M/G/c queue

1981 ◽  
Vol 13 (1) ◽  
pp. 186-206 ◽  
Author(s):  
H. C. Tijms ◽  
M. H. Van Hoorn ◽  
A. Federgruen
Keyword(s):  
Steady State ◽  
Queue Size ◽  
Numerical Experience ◽  
General Service Times ◽  
Server Queue ◽  
Poisson Arrivals ◽  
The Mean ◽  
Multi Server ◽  
General Service ◽  
Steady State Probabilities

For the multi-server queue with Poisson arrivals and general service times we present various approximations for the steady-state probabilities of the queue size. These approximations are computed from numerically stable recursion schemes which can be easily applied in practice. Numerical experience reveals that the approximations are very accurate with errors typically below 5%. For the delay probability the various approximations result either into the widely used Erlang delay probability or into a new approximation which improves in many cases the Erlang delay probability approximation. Also for the mean queue size we find a new approximation that turns out to be a good approximation for all values of the queueing parameters including the coefficient of variation of the service time.

On a decomposition result for a class of vacation queueing systems

1990 ◽  
Vol 27 (01) ◽  
pp. 227-231 ◽  
Author(s):  
Jacqueline Loris-Teghem
Keyword(s):  
Steady State ◽  
Time Distribution ◽  
Queueing Systems ◽  
Single Server ◽  
Service Time Distribution ◽  
Steady State Distribution ◽  
State Distribution ◽  
Random Size ◽  
Poisson Arrivals ◽  
General Service

We consider a single-server infinite-capacity queueing sysem with Poisson arrivals of customer groups of random size and a general service time distribution, the server of which applies a general exhaustive service vacation policy. We are concerned with the steady-state distribution of the actual waiting time of a customer arriving while the server is active.

Approximations for the steady-state probabilities in the M/G/c queue

1981 ◽  
Vol 13 (01) ◽  
pp. 186-206 ◽  
Author(s):  
H. C. Tijms ◽  
M. H. Van Hoorn ◽  
A. Federgruen
Keyword(s):  
Steady State ◽  
Queue Size ◽  
Numerical Experience ◽  
General Service Times ◽  
Server Queue ◽  
Poisson Arrivals ◽  
The Mean ◽  
Multi Server ◽  
General Service ◽  
Steady State Probabilities

For the multi-server queue with Poisson arrivals and general service times we present various approximations for the steady-state probabilities of the queue size. These approximations are computed from numerically stable recursion schemes which can be easily applied in practice. Numerical experience reveals that the approximations are very accurate with errors typically below 5%. For the delay probability the various approximations result either into the widely used Erlang delay probability or into a new approximation which improves in many cases the Erlang delay probability approximation. Also for the mean queue size we find a new approximation that turns out to be a good approximation for all values of the queueing parameters including the coefficient of variation of the service time.

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
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