A single server retrial G-line along preemptive resume priority & non-continuous server as per Bernoulli vacation

2022 ◽  
Author(s):  
K. Geetha Priya ◽  
L. Francis Raj
Keyword(s):  
Single Server ◽  
Preemptive Resume ◽  
Preemptive Resume Priority ◽  
Bernoulli Vacation

scholarly journals On a generalization of the preemptive resume priority

1986 ◽  
Vol 18 (01) ◽  
pp. 255-273
Author(s):  
Philippe Nain
Keyword(s):  
Communication Networks ◽  
Queueing System ◽  
Single Server ◽  
Stieltjes Transform ◽  
Priority Service ◽  
Service Interruption ◽  
Preemptive Resume ◽  
Class 1 ◽  
Potential Applications ◽  
Preemptive Resume Priority

This paper considers a queueing system with two classes of customers and a single server, where the service policy is of threshold type. As soon as the amount of work required by the class 1 customers is greater than a fixed threshold, the class 1 customers get the server's attention; otherwise the class 2 customers have the priority. Service interruptions can occur for both classes of customers on the basis of the above description of the service mechanism, and in this case the service interruption discipline is preemptive resume priority (PRP). This model, which turns out to be a generalization of the PRP queueing system, has potential applications in computer systems and in communication networks. For Poisson inputs, exponential (arbitrary) servicetime distribution for class 1 (class 2) customers, we derive the Laplace–Stieltjes transform of the stationary joint distribution of the workload of the server, by reducing the analysis to the resolution of a boundary value problem. Explicit formulas are obtained.

scholarly journals On a generalization of the preemptive resume priority

1986 ◽  
Vol 18 (1) ◽  
pp. 255-273 ◽  
Author(s):  
Philippe Nain
Keyword(s):  
Communication Networks ◽  
Queueing System ◽  
Single Server ◽  
Stieltjes Transform ◽  
Priority Service ◽  
Service Interruption ◽  
Preemptive Resume ◽  
Class 1 ◽  
Potential Applications ◽  
Preemptive Resume Priority

This paper considers a queueing system with two classes of customers and a single server, where the service policy is of threshold type. As soon as the amount of work required by the class 1 customers is greater than a fixed threshold, the class 1 customers get the server's attention; otherwise the class 2 customers have the priority. Service interruptions can occur for both classes of customers on the basis of the above description of the service mechanism, and in this case the service interruption discipline is preemptive resume priority (PRP). This model, which turns out to be a generalization of the PRP queueing system, has potential applications in computer systems and in communication networks. For Poisson inputs, exponential (arbitrary) servicetime distribution for class 1 (class 2) customers, we derive the Laplace–Stieltjes transform of the stationary joint distribution of the workload of the server, by reducing the analysis to the resolution of a boundary value problem. Explicit formulas are obtained.

scholarly journals Diffusion Model of Preemptive-Resume Priority Systems and Its Application to Performance Evaluation of SDN Switches

Sensors ◽  
2021 ◽  
Vol 21 (15) ◽  
pp. 5042
Author(s):  
Tomasz Nycz ◽  
Tadeusz Czachórski ◽  
Monika Nycz
Keyword(s):  
Diffusion Approximation ◽  
Numerical Models ◽  
Software Defined Networks ◽  
Detailed Model ◽  
Preemptive Resume ◽  
Central Controller ◽  
Priority Systems ◽  
Primary Element ◽  
Preemptive Resume Priority ◽  
General Distributions

The increasing use of Software-Defined Networks brings the need for their performance analysis and detailed analytical and numerical models of them. The primary element of such research is a model of a SDN switch. This model should take into account non-Poisson traffic and general distributions of service times. Because of frequent changes in SDN flows, it should also analyze transient states of the queues. The method of diffusion approximation can meet these requirements. We present here a diffusion approximation of priority queues and apply it to build a more detailed model of SDN switch where packets returned by the central controller have higher priority than other packets.

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.

Performance Analysis of an M/G/1 Feedback Retrial Queue with Two Types of Service and Bernoulli Vacation

2016 ◽  
pp. 38-54
Author(s):  
Arivudainambi D ◽  
Gowsalya Mahalingam
Keyword(s):  
Retrial Queue ◽  
Single Server ◽  
Supplementary Variable ◽  
Number Of Customers ◽  
Bernoulli Schedule ◽  
Schedule Mechanism ◽  
Fcfs Discipline ◽  
Bernoulli Vacation

This chapter is concerned with the analysis of a single server retrial queue with two types of service, Bernoulli vacation and feedback. The server provides two types of service i.e., type 1 service with probability??1 and type 2 service with probability ??2. We assume that the arriving customer who finds the server busy upon arrival leaves the service area and are queued in the orbit in accordance with an FCFS discipline and repeats its request for service after some random time. After completion of type 1 or type 2 service the unsatisfied customer can feedback and joins the tail of the retrial queue with probability f or else may depart from the system with probability 1–f. Further the server takes vacation under Bernoulli schedule mechanism, i.e., after each service completion the server takes a vacation with probability q or with probability p waits to serve the next customer. For this queueing model, the steady state distributions of the server state and the number of customers in the orbit are obtained using supplementary variable technique. Finally the average number of customers in the system and average number of customers in the orbit are also obtained.

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