scholarly journals Geo/Geo/1/N Queue with In-Immune and Immune Service Killing Discipline

2012 ◽  
Vol 23 (1) ◽  
pp. 129-148
Author(s):  
Madhu Jain Madhu Jain
Keyword(s):  
Performance Measures ◽  
Generating Functions ◽  
Relaxation Method ◽  
Single Server ◽  
Finite Capacity ◽  
Single Server Queue ◽  
Stationary Probability Distribution ◽  
Negative Customers ◽  
Server Queue ◽  
Successive Over Relaxation

The present investigation studies a discrete time single server queue with both positive and negative arrival streams in accordance with removal of the customer from the end (RCE)-in immune and immune service killing policy. This study is a generalization of the queue with negative customers, wherein only positive customers need a service and negative customers arriving to the system can kill the already present positive customers from any where in the queue, otherwise get lost. The concept of both in-immune and immune service killing are taken into consideration. According to the in-immune killing policy, the negative customer is allowed to kill the most recent positive customer inspite of whether it is in service or not, while the immune service killing discipline suggests that the customer currently being served is immune from killing by the negative arrival. We analyze a queue with geometric arrivals of both positive and negative customers for a finite capacity system. The stationary probability distribution and other performance measures are derived in terms of the generating functions. The results so obtained are validated by the numerical method based on successive over relaxation method (SOR). We have also employed the neurro fuzzy approach for exhibiting the approximate results for various performance measures.

Sojourn times in single-server queues by negative customers

1993 ◽  
Vol 30 (4) ◽  
pp. 943-963 ◽  
Author(s):  
P. G. Harrison ◽  
E. Pitel
Keyword(s):  
Laplace Transform ◽  
Single Server ◽  
Processor Sharing ◽  
Single Server Queue ◽  
Negative Customers ◽  
Mean Values ◽  
Poisson Arrival ◽  
Server Queue ◽  
The Laplace Transform ◽  
Time Density

We derive expressions for the Laplace transform of the sojourn time density in a single-server queue with exponential service times and independent Poisson arrival streams of both ordinary, positive customers and negative customers which eliminate a positive customer if present. We compare first-come first-served and last-come first-served queueing disciplines for the positive customers, combined with elimination of the last customer in the queue or the customer in service by a negative customer. We also derive the corresponding result for processor-sharing discipline with random elimination. The results show differences not only in the Laplace transforms but also in the means of the distributions, in contrast to the case where there are no negative customers. The various combinations of queueing discipline and elimination strategy are ranked with respect to these mean values.

scholarly journals Stationary queue length of a single-server queue with negative arrivals and nonexponential service time distributions

2018 ◽  
Vol 189 ◽  
pp. 02006 ◽  
Author(s):  
S K Koh ◽  
C H Chin ◽  
Y F Tan ◽  
L E Teoh ◽  
A H Pooi ◽  
...  
Keyword(s):  
Service Time ◽  
Queue Length ◽  
Queueing Systems ◽  
Length Distribution ◽  
Single Server ◽  
Service Time Distribution ◽  
Single Server Queue ◽  
Negative Customers ◽  
Stationary Queue Length ◽  
Server Queue

In this paper, a single-server queue with negative customers is considered. The arrival of a negative customer will remove one positive customer that is being served, if any is present. An alternative approach will be introduced to derive a set of equations which will be solved to obtain the stationary queue length distribution. We assume that the service time distribution tends to a constant asymptotic rate when time t goes to infinity. This assumption will allow for finding the stationary queue length of queueing systems with non-exponential service time distributions. Numerical examples for gamma distributed service time with fractional value of shape parameter will be presented in which the steady-state distribution of queue length with such service time distributions may not be easily computed by most of the existing analytical methods.

A finite capacity single-server queue with customer loss

1986 ◽  
Vol 2 (1) ◽  
pp. 97-121 ◽  
Author(s):  
C. Knessl ◽  
B. J. Matkowsky ◽  
Z. Schuss ◽  
C. Tier
Keyword(s):  
Single Server ◽  
Finite Capacity ◽  
Single Server Queue ◽  
Server Queue

Sojourn times in single-server queues by negative customers

1993 ◽  
Vol 30 (04) ◽  
pp. 943-963
Author(s):  
P. G. Harrison ◽  
E. Pitel
Keyword(s):  
Laplace Transform ◽  
Single Server ◽  
Processor Sharing ◽  
Single Server Queue ◽  
Negative Customers ◽  
Mean Values ◽  
Poisson Arrival ◽  
Server Queue ◽  
The Laplace Transform ◽  
Time Density

We derive expressions for the Laplace transform of the sojourn time density in a single-server queue with exponential service times and independent Poisson arrival streams of both ordinary, positive customers and negative customers which eliminate a positive customer if present. We compare first-come first-served and last-come first-served queueing disciplines for the positive customers, combined with elimination of the last customer in the queue or the customer in service by a negative customer. We also derive the corresponding result for processor-sharing discipline with random elimination. The results show differences not only in the Laplace transforms but also in the means of the distributions, in contrast to the case where there are no negative customers. The various combinations of queueing discipline and elimination strategy are ranked with respect to these mean values.

A Light Traffic Approximation for a Single-Server Queue

1984 ◽  
Vol 9 (4) ◽  
pp. 624-628 ◽  
Author(s):  
D. J. Daley ◽  
T. Rolski
Keyword(s):  
Single Server ◽  
Single Server Queue ◽  
Light Traffic ◽  
Server Queue
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