On the work load process in a general preemptive resume priority queue

1972 ◽  
Vol 9 (3) ◽  
pp. 588-603 ◽  
Author(s):  
R. Schassberger
Keyword(s):  
Distribution Function ◽  
Work Load ◽  
Priority Queue ◽  
General Distribution ◽  
Time Service ◽  
Service Unit ◽  
System A ◽  
Preemptive Resume ◽  
Preemptive Resume Priority ◽  
Method Of Phases

Consider the following queuing system: A sequence of customers arrive at a service unit in a recurrent stream. A customer is of priority k with probability πk, k = 1, …, n. A class i customer preempts service of class k, k > i. Interrupted service is resumed without loss or gain in service time. Service is FIFO within classes. Service times for class k are drawn from a general distribution function Bk(t).Using the method of phases and a resolution technique from the theory of Markov processes we obtain Laplace transforms of various distributions.

On the work load process in a general preemptive resume priority queue

1972 ◽  
Vol 9 (03) ◽  
pp. 588-603 ◽  
Author(s):  
R. Schassberger
Keyword(s):  
Distribution Function ◽  
Work Load ◽  
Priority Queue ◽  
General Distribution ◽  
Time Service ◽  
Service Unit ◽  
System A ◽  
Preemptive Resume ◽  
Preemptive Resume Priority ◽  
Method Of Phases

Consider the following queuing system: A sequence of customers arrive at a service unit in a recurrent stream. A customer is of priority k with probability πk , k = 1, …, n. A class i customer preempts service of class k, k > i. Interrupted service is resumed without loss or gain in service time. Service is FIFO within classes. Service times for class k are drawn from a general distribution function Bk (t). Using the method of phases and a resolution technique from the theory of Markov processes we obtain Laplace transforms of various distributions.

Basic analysis of a head-of-the-line priority queue with renewal type input

1975 ◽  
Vol 12 (2) ◽  
pp. 346-352
Author(s):  
R. Schassberger
Keyword(s):  
Distribution Function ◽  
Priority Queue ◽  
General Distribution ◽  
Single Server ◽  
Service Times

A single server is fed by a renewal stream of individual customers. These are of type k with probability πk, k = 1, …, N, and are all served individually. Upon completion of a service the server proceeds immediately with a customer of the lowest type (= highest priority) present, if any. Service times for type k are drawn from a general distribution function Bk(t) concentrated on (0, ∞).We lay the foundations for a broad analysis of the model.

Preemptive Resume Priority Queue

1961 ◽  
Vol 9 (5) ◽  
pp. 732-742 ◽  
Author(s):  
N. K. Jaiswal
Keyword(s):  
Priority Queue ◽  
Preemptive Resume ◽  
Preemptive Resume Priority

Basic analysis of a head-of-the-line priority queue with renewal type input

1975 ◽  
Vol 12 (02) ◽  
pp. 346-352 ◽  
Author(s):  
R. Schassberger
Keyword(s):  
Distribution Function ◽  
Priority Queue ◽  
General Distribution ◽  
Single Server ◽  
Service Times

A single server is fed by a renewal stream of individual customers. These are of type k with probability πk, k = 1, …, N, and are all served individually. Upon completion of a service the server proceeds immediately with a customer of the lowest type (= highest priority) present, if any. Service times for type k are drawn from a general distribution function Bk (t) concentrated on (0, ∞). We lay the foundations for a broad analysis of the model.

scholarly journals The MAP, M/G1,G2/1 queue with preemptive priority

1997 ◽  
Vol 10 (4) ◽  
pp. 407-421 ◽  
Author(s):  
Bong Dae Choi ◽  
Gang Uk Hwang
Keyword(s):  
Service Time ◽  
Probability Generating Function ◽  
Priority Queue ◽  
Arrival Process ◽  
Supplementary Variable ◽  
Preemptive Priority ◽  
Preemptive Resume ◽  
Preemptive Resume Priority ◽  
Number Of Customers ◽  
Time Density

We consider the MAP, M/G1,G2/1 queue with preemptive resume priority, where low priority customers arrive to the system according to a Markovian arrival process (MAP) and high priority customers according to a Poisson process. The service time density function of low (respectively: high) priority customers is g1(x) (respectively: g2(x)). We use the supplementary variable method with Extended Laplace Transforms to obtain the joint transform of the number of customers in each priority queue, as well as the remaining service time for the customer in service in the steady state. We also derive the probability generating function for the number of customers of low (respectively, high) priority in the system just after the service completion epochs for customers of low (respectively, high) priority.

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.

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