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.

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.

On the single-server queue with the preemptive-resume last-come–first-served queue discipline

1986 ◽  
Vol 23 (01) ◽  
pp. 243-248
Author(s):  
D. Fakinos
Keyword(s):  
Equilibrium Distribution ◽  
Queueing System ◽  
Independent Random Variables ◽  
Single Server ◽  
Queue Size ◽  
Single Server Queue ◽  
Idle Period ◽  
Preemptive Resume ◽  
Server Queue ◽  
Queue Discipline

The paper considers the GI/G/1 queueing system under the assumption of a last-come–first-served queue discipline, where each customer begins service immediately upon his arrival. At the next arrival, the previous service is interrupted but no loss of service is involved. It has been shown that when the system is considered exclusively at arrival epochs or exclusively at departure epochs, then the equilibrium distribution of the queue-size is geometric, while the remaining durations of the corresponding services are independent random variables each one distributed as the idle period in the dual (inverse) queue. In this paper alternative simpler proofs of the above results are given.

On the single-server queue with the preemptive-resume last-come–first-served queue discipline

1986 ◽  
Vol 23 (1) ◽  
pp. 243-248 ◽  
Author(s):  
D. Fakinos
Keyword(s):  
Equilibrium Distribution ◽  
Queueing System ◽  
Independent Random Variables ◽  
Single Server ◽  
Queue Size ◽  
Single Server Queue ◽  
Idle Period ◽  
Preemptive Resume ◽  
Server Queue ◽  
Queue Discipline

The paper considers the GI/G/1 queueing system under the assumption of a last-come–first-served queue discipline, where each customer begins service immediately upon his arrival. At the next arrival, the previous service is interrupted but no loss of service is involved. It has been shown that when the system is considered exclusively at arrival epochs or exclusively at departure epochs, then the equilibrium distribution of the queue-size is geometric, while the remaining durations of the corresponding services are independent random variables each one distributed as the idle period in the dual (inverse) queue. In this paper alternative simpler proofs of the above results are given.

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.

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.

scholarly journals Single-Server Queue with Markov-Dependent Inter-Arrival and Service Times

2006 ◽  
Vol 54 (1) ◽  
pp. 79-79
Author(s):  
I. J. B. F. Adan ◽  
V. G. Kulkarni
Keyword(s):  
Single Server ◽  
Single Server Queue ◽  
Server Queue ◽  
Service Times

The single-server queue with independent GI/G and M/G input streams

1987 ◽  
Vol 19 (1) ◽  
pp. 266-286 ◽  
Author(s):  
Teunis J. Ott
Keyword(s):  
Distribution Function ◽  
Numerical Analysis ◽  
Real Time ◽  
Queueing System ◽  
Single Server ◽  
Equivalent System ◽  
Single Server Queue ◽  
Input Stream ◽  
Server Queue ◽  
Single Input

This paper studies the single-server queueing system with two independent input streams: a GI/G and an M/G stream. A new proof is given of an old result which shows how this system can be transformed into an equivalent ‘single input stream’ GI/G/1 queue, and methods to study that equivalent system numerically are given. As part of the numerical analysis, algorithms are given to compute the moments and the distribution function of busy periods in the M/G/1 queue, and of other related busy periods. Special attention is given to the single-server queue with independent D/G and M/G input streams.This work is to be used in the modeling of real-time computer systems, which can often be described as a single-server queueing system with independent D/G and M/G input streams, see for example Ott (1984b).

scholarly journals Stochastic analysis of the departure and quasi-input processes in a versatile single-server queue

1996 ◽  
Vol 9 (2) ◽  
pp. 171-183 ◽  
Author(s):  
J. R. Artalejo ◽  
A. Gomez-Corral
Keyword(s):  
Markov Chain ◽  
Stochastic Analysis ◽  
Queueing System ◽  
Single Server ◽  
Structural Form ◽  
Single Server Queue ◽  
Server Queue ◽  
Negative Exponential ◽  
Orbit Size ◽  
Negative Arrivals

This paper is concerned with the stochastic analysis of the departure and quasi-input processes of a Markovian single-server queue with negative exponential arrivals and repeated attempts. Our queueing system is characterized by the phenomenon that a customer who finds the server busy upon arrival joins an orbit of unsatisfied customers. The orbiting customers form a queue such that only a customer selected according to a certain rule can reapply for service. The intervals separating two successive repeated attempts are exponentially distributed with rate α+jμ, when the orbit size is j≥1. Negative arrivals have the effect of killing some customer in the orbit, if one is present, and they have no effect otherwise. Since customers can leave the system without service, the structural form of type M/G/1 is not preserved. We study the Markov chain with transitions occurring at epochs of service completions or negative arrivals. Then we investigate the departure and quasi-input processes.

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