On a single-server queue with group arrivals

1976 ◽  
Vol 13 (3) ◽  
pp. 619-622 ◽  
Author(s):  
J. W. Cohen
Keyword(s):  
Waiting Time ◽  
Queueing System ◽  
Limiting Distribution ◽  
Single Server ◽  
Waiting Time Distribution ◽  
Single Server Queue ◽  
Regenerative Processes ◽  
Virtual Waiting Time ◽  
Server Queue ◽  
Individual Service

The queueing system GI/G/1 with group arrivals and individual service of the customers is considered. For the stable situation the limiting distribution of the waiting time distribution of the kth served customer for k → ∞ is derived by using the theory of regenerative processes. It is assumed that the group sizes are i.i.d. variables of which the distribution is aperiodic. The relation between this limiting distribution and the stationary distribution of the virtual waiting time is derived.

On a single-server queue with group arrivals

1976 ◽  
Vol 13 (03) ◽  
pp. 619-622 ◽  
Author(s):  
J. W. Cohen
Keyword(s):  
Waiting Time ◽  
Queueing System ◽  
Limiting Distribution ◽  
Single Server ◽  
Waiting Time Distribution ◽  
Single Server Queue ◽  
Regenerative Processes ◽  
Virtual Waiting Time ◽  
Server Queue ◽  
Individual Service

The queueing system GI/G/1 with group arrivals and individual service of the customers is considered. For the stable situation the limiting distribution of the waiting time distribution of the kth served customer for k → ∞ is derived by using the theory of regenerative processes. It is assumed that the group sizes are i.i.d. variables of which the distribution is aperiodic. The relation between this limiting distribution and the stationary distribution of the virtual waiting time is derived.

The single-server queue with service depending on queue size and with the preemptive-resume last-come–first-served queue discipline

1987 ◽  
Vol 24 (03) ◽  
pp. 758-767
Author(s):  
D. Fakinos
Keyword(s):  
Queueing System ◽  
Limiting Distribution ◽  
Single Server ◽  
Queue Size ◽  
Single Server Queue ◽  
Preemptive Resume ◽  
Server Queue ◽  
Queue Discipline ◽  
Service Times

This paper studies theGI/G/1 queueing system assuming that customers have service times depending on the queue size and also that they are served in accordance with the preemptive-resume last-come–first-served queue discipline. Expressions are given for the limiting distribution of the queue size and the remaining durations of the corresponding services, when the system is considered at arrival epochs, at departure epochs and continuously in time. Also these results are applied to some particular cases of the above queueing system.

Single-server queues with impatient customers

1984 ◽  
Vol 16 (4) ◽  
pp. 887-905 ◽  
Author(s):  
F. Baccelli ◽  
P. Boyer ◽  
G. Hebuterne
Keyword(s):  
Waiting Time ◽  
Queueing System ◽  
Distribution Functions ◽  
Single Server ◽  
Waiting Time Distribution ◽  
Input Process ◽  
Poisson Input ◽  
Virtual Waiting Time ◽  
Random Threshold ◽  
The Stability

We consider a single-server queueing system in which a customer gives up whenever his waiting time is larger than a random threshold, his patience time. In the case of a GI/GI/1 queue with i.i.d. patience times, we establish the extensions of the classical GI/GI/1 formulae concerning the stability condition and the relation between actual and virtual waiting-time distribution functions. We also prove that these last two distribution functions coincide in the case of a Poisson input process and determine their common law.

scholarly journals An M/G/1 queue with multiple types of feedback and gated vacations

1997 ◽  
Vol 34 (03) ◽  
pp. 773-784 ◽  
Author(s):  
Onno J. Boxma ◽  
Uri Yechiali
Keyword(s):  
Waiting Time ◽  
Service Time ◽  
Queue Length ◽  
Time Distribution ◽  
Single Server ◽  
Service Time Distribution ◽  
Waiting Time Distribution ◽  
Single Server Queue ◽  
Server Queue ◽  
Poisson Arrivals

This paper considers a single-server queue with Poisson arrivals and multiple customer feedbacks. If the first service attempt of a newly arriving customer is not successful, he returns to the end of the queue for another service attempt, with a different service time distribution. He keeps trying in this manner (as an ‘old' customer) until his service is successful. The server operates according to the ‘gated vacation' strategy; when it returns from a vacation to find K (new and old) customers, it renders a single service attempt to each of them and takes another vacation, etc. We study the joint queue length process of new and old customers, as well as the waiting time distribution of customers. Some extensions are also discussed.

Exponential expansion for the tail of the waiting-time probability in the single-server queue with batch arrivals

1988 ◽  
Vol 20 (4) ◽  
pp. 880-895 ◽  
Author(s):  
J. C. W. Van Ommeren
Keyword(s):  
Waiting Time ◽  
Interarrival Time ◽  
Single Server ◽  
Waiting Time Distribution ◽  
Single Server Queue ◽  
Batch Arrivals ◽  
Exponential Expansion ◽  
Phase Type ◽  
Phase Type Distributions ◽  
Server Queue

This paper deals with the single-server queue with batch arrivals. We show that under suitable conditions the waiting-time distribution of an individual customer has an asymptotically exponential expansion. Computationally useful characterizations of the amplitude factor and the decay parameter are given for the practically important case in which the interarrival time and the service time have phase-type distributions.

Stochastic bounds for the single-server queue

1976 ◽  
Vol 80 (3) ◽  
pp. 521-525 ◽  
Author(s):  
J. Köllerström
Keyword(s):  
Waiting Time ◽  
Time Distribution ◽  
Infinite Divisibility ◽  
Single Server ◽  
Traffic Intensity ◽  
Waiting Time Distribution ◽  
Single Server Queue ◽  
Exponential Tail ◽  
Server Queue ◽  
Fitting In

Various elegant properties have been found for the waiting time distribution G for the queue GI/G/1 in statistical equilibrium, such as infinite divisibility ((1), p. 282) and that of having an exponential tail ((11), (2), p. 411, (1), p. 324). Here we derive another property which holds quite generally, provided the traffic intensity ρ < 1, and which is extremely simple, fitting in with the above results as well as yielding some useful properties in the form of upper and lower stochastic bounds for G which augment the bounds obtained by Kingman (5), (6), (8) and by Ross (10).

The single-server queue with service depending on queue size and with the preemptive-resume last-come–first-served queue discipline

1987 ◽  
Vol 24 (3) ◽  
pp. 758-767 ◽  
Author(s):  
D. Fakinos
Keyword(s):  
Queueing System ◽  
Limiting Distribution ◽  
Single Server ◽  
Queue Size ◽  
Single Server Queue ◽  
Preemptive Resume ◽  
Server Queue ◽  
Queue Discipline ◽  
Service Times

This paper studies the GI/G/1 queueing system assuming that customers have service times depending on the queue size and also that they are served in accordance with the preemptive-resume last-come–first-served queue discipline. Expressions are given for the limiting distribution of the queue size and the remaining durations of the corresponding services, when the system is considered at arrival epochs, at departure epochs and continuously in time. Also these results are applied to some particular cases of the above queueing system.

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