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 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.

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.

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.

A note on the queueing system GI/Ek/1

1969 ◽  
Vol 6 (3) ◽  
pp. 708-710 ◽  
Author(s):  
P. D. Finch
Keyword(s):  
Time Distribution ◽  
Queueing System ◽  
Single Server ◽  
Service Time Distribution ◽  
Alternative Procedure ◽  
Single Server Queue ◽  
Server Queue ◽  
Image Position ◽  
The Right ◽  
Similar Evaluation

In this note we adopt the notation and terminology of Kingman (1966) without further comment. For the general single server queue one has For the queueing system GI/Ek/1 it is possible to make use of the particular nature of the service time distribution to evaluate the right-hand side of Equation (1) in terms of the k roots of a certain equation. This evaluation is carried out in detail in Prabhu (1965) to which reference should be made for the technicalities involved. A similar evaluation applies to the limiting distribution when it exists. However, the resulting expression again involves the k roots of a certain equation. In this note we draw attention to an alternative procedure which does not involve the calculation of roots. We remark that a similar, but slightly different, procedure can be used in the study of the queueing system Ek/GI/1. Details of this will be presented in a separate note.

scholarly journals The transient behaviour of the queueing system Gi/M/1

1963 ◽  
Vol 3 (2) ◽  
pp. 249-256 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Distribution Function ◽  
Explicit Expression ◽  
Queueing System ◽  
Single Server ◽  
Single Server Queue ◽  
Transient Behaviour ◽  
Special Cases ◽  
Server Queue ◽  
Interarrival Times ◽  
Lagrange Series

SUMMARYWe consider a single server queue for which the interarrival times are identically and independently distributed with distribution function A(x) and whose service times are distributed independently of each other and of the interarrival times with distribution function B(x) = 1 − e−x, x ≧ 0. We suppose that the system starts from emptiness and use the results of P. D. Finch [2] to derive an explicit expression for qnj, the probability that the (n + 1)th arrival finds more than j customers in the system. The special cases M/M/1 and D/M/1 are considerend and it is shown in the general case that qnj is a partial sum of the usual Lagrange series for the limiting probability .

Weak convergence theorems for priority queues: preemptive-resume discipline

1971 ◽  
Vol 8 (1) ◽  
pp. 74-94 ◽  
Author(s):  
Ward Whitt
Keyword(s):  
Weak Convergence ◽  
Service Time ◽  
Priority Queues ◽  
Single Server ◽  
Single Server Queue ◽  
Convergence Theorems ◽  
Lower Priority ◽  
Preemptive Resume ◽  
Server Queue ◽  
Customer Returns

We shall consider a single-server queue with r priority classes of customers and a preemptive-resume discipline. In this system customers are served in order of their priority while customers of the same priority are served in order of their arrival. Higher priority customers, immediately upon arrival, replace lower priority customers at the server, while customers displaced in this way return to the server before any other customers of the same priority receive service. When a displaced customer returns to the server, his remaining service time is the uncompleted portion of his original service time (cf. Jaiswal (1968)).

scholarly journals A single server queue under random vacation policy

2019 ◽  
Author(s):  
Priyanka kalita ◽  
Gautam Choudhury
Keyword(s):  
Steady State ◽  
Lower Cost ◽  
Queueing System ◽  
System Size ◽  
Mean Value ◽  
Single Server ◽  
Idle Period ◽  
System A ◽  
Server Queue ◽  
Number Of Customers

This paper deals with an M/G/1 queueing system with random vacation policy, in which the server takes the maximum number of random vacations till it finds minimum one message (customer) waiting in a queue at a vacation completion epoch. If no arrival occurs after completing maximum number of random vacations, the server stays dormant in the system and waits for the upcoming arrival. Here, we obtain steady state queue size distribution at an idle period completion epoch and service completion epoch. We also obtain the steady state system size probabilities and system state probabilities. Some significant measures such as a mean number of customers served during the busy period, Laplace-Stieltjes transform of unfinished work and its corresponding mean value and second moment have been obtained for the system. A cost optimal policy have been developed in terms of the average cost function to determine a locally optimal random vacation policy at a lower cost. Finally, we present various numerical results for the above system performance measures.

On a Single Server Queue

1965 ◽  
Vol 14 (3-4) ◽  
pp. 163-166 ◽  
Author(s):  
D. N. Shanbhag
Keyword(s):  
Stationary State ◽  
Waiting Time ◽  
Queueing System ◽  
Alternative Proof ◽  
Single Server ◽  
Single Server Queue ◽  
State Distribution ◽  
Simple Method ◽  
Server Queue

Summary: In this note all alternative proof of Lindley's (1952) theorem for the existence of the stationary state distribution of the waiting time of a customer in the queueing system GI/G/1 is given. Further, a direct and simple method is given for deriving the stationary state distribution of the waiting time in the queueing system GI/M/1.

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