scholarly journals On the independence of sojourn times in tandem queues

1989 ◽  
Vol 21 (2) ◽  
pp. 488-489 ◽  
Author(s):  
Thomas M. Chen
Keyword(s):  
Tandem Queues ◽  
Sojourn Times ◽  
Deterministic Service ◽  
Service Times

Reich (1957) proved that the sojourn times in two tandem queues are independent when the first queue is M/M /1 and the second has exponential service times. When service times in the first queue are not exponential, it has been generally expected that the sojourn times are not independent. A proof for the case of deterministic service times in the first queue is offered here.

scholarly journals On the independence of sojourn times in tandem queues

1989 ◽  
Vol 21 (02) ◽  
pp. 488-489
Author(s):  
Thomas M. Chen
Keyword(s):  
Tandem Queues ◽  
Sojourn Times ◽  
Deterministic Service ◽  
Service Times

Reich (1957) proved that the sojourn times in two tandem queues are independent when the first queue is M/M /1 and the second has exponential service times. When service times in the first queue are not exponential, it has been generally expected that the sojourn times are not independent. A proof for the case of deterministic service times in the first queue is offered here.

The dependence of sojourn times on service times in tandem queues

1984 ◽  
Vol 21 (3) ◽  
pp. 661-667 ◽  
Author(s):  
Xi-Ren Cao
Keyword(s):  
Sojourn Time ◽  
Past History ◽  
Interarrival Time ◽  
Conditional Probabilities ◽  
Tandem Queues ◽  
Sojourn Times ◽  
Distributed Service ◽  
Service Times

In this paper we study a series of servers with exponentially distributed service times. We find that the sojourn time of a customer at any server depends on the customer's past history only through the customer's interarrival time to that server. A method of calculating the conditional probabilities of sojourn times is developed.

scholarly journals NOTE ON APPROXIMATIONS FOR THE MULTISERVER QUEUE WITH FINITE BUFFER AND DETERMINISTIC SERVICES

2008 ◽  
Vol 22 (4) ◽  
pp. 653-658 ◽  
Author(s):  
Henk Tijms
Keyword(s):  
Performance Measures ◽  
Service Time ◽  
Finite Buffer ◽  
Two Phase ◽  
Sojourn Times ◽  
Deterministic Service ◽  
Service Times ◽  
Phase Process

This article shows that very accurate accurate approximations to performance measures in the multiserver M/D/c/c+N queue with finite buffer and deterministic service times can be obtained by replacing the deterministic service time by a two-phase process with exponential sojourn times and branching probabilities outside the interval [0, 1].

The dependence of sojourn times on service times in tandem queues

1984 ◽  
Vol 21 (03) ◽  
pp. 661-667
Author(s):  
Xi-Ren Cao
Keyword(s):  
Sojourn Time ◽  
Past History ◽  
Interarrival Time ◽  
Conditional Probabilities ◽  
Tandem Queues ◽  
Sojourn Times ◽  
Distributed Service ◽  
Service Times

In this paper we study a series of servers with exponentially distributed service times. We find that the sojourn time of a customer at any server depends on the customer's past history only through the customer's interarrival time to that server. A method of calculating the conditional probabilities of sojourn times is developed.

Bounds for the expected delays in some tandem queues

1980 ◽  
Vol 17 (03) ◽  
pp. 831-838 ◽  
Author(s):  
Shun-Chen Niu
Keyword(s):  
Upper Bound ◽  
Renewal Process ◽  
Arrival Process ◽  
Tandem Queues ◽  
Service Distribution ◽  
Deterministic Service ◽  
Service Times ◽  
Constant Service Times ◽  
General Service

Tandem queues are analyzed. An upper bound for the stationary expected delay in front of the second server is found for a sequence of two queues in tandem where the first server has deterministic service times, the second server has general service distribution, and the arrival process is an arbitrary renewal process. The result is extended to the case of n queues in tandem where all the servers except the last one have constant service times.

scholarly journals Tandem queues with deterministic service times

1994 ◽  
Vol 49 (1) ◽  
pp. 221-239 ◽  
Author(s):  
O. J. Boxma ◽  
J. A. C. Resing
Keyword(s):  
Tandem Queues ◽  
Deterministic Service ◽  
Service Times

Bounds for the expected delays in some tandem queues

1980 ◽  
Vol 17 (3) ◽  
pp. 831-838 ◽  
Author(s):  
Shun-Chen Niu
Keyword(s):  
Upper Bound ◽  
Renewal Process ◽  
Arrival Process ◽  
Tandem Queues ◽  
Service Distribution ◽  
Deterministic Service ◽  
Service Times ◽  
Constant Service Times ◽  
General Service

Tandem queues are analyzed. An upper bound for the stationary expected delay in front of the second server is found for a sequence of two queues in tandem where the first server has deterministic service times, the second server has general service distribution, and the arrival process is an arbitrary renewal process. The result is extended to the case of n queues in tandem where all the servers except the last one have constant service times.

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