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.

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.

A service model in which the server is required to search for customers

1984 ◽  
Vol 21 (1) ◽  
pp. 157-166 ◽  
Author(s):  
Marcel F. Neuts ◽  
M. F. Ramalhoto
Keyword(s):  
Poisson Process ◽  
Numerical Computation ◽  
Probability Distributions ◽  
General Distribution ◽  
Search Process ◽  
Single Server ◽  
Stationary Probability ◽  
Service Model ◽  
Service Times ◽  
Number Of Customers

Customers enter a pool according to a Poisson process and wait there to be found and processed by a single server. The service times of successive items are independent and have a common general distribution. Successive services are separated by seek phases during which the server searches for the next customer. The search process is Markovian and the probability of locating a customer in (t, t + dt) is proportional to the number of customers in the pool at time t. Various stationary probability distributions for this model are obtained in explicit forms well-suited for numerical computation.Under the assumption of exponential service times, corresponding results are obtained for the case where customers may escape from the pool.

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.

scholarly journals The stationary local sojourn time in single server tandem queues with renewal input

1999 ◽  
Vol 12 (4) ◽  
pp. 417-428
Author(s):  
Pierre Le Gall
Keyword(s):  
Sojourn Time ◽  
Stationary Regime ◽  
General Distribution ◽  
Single Server ◽  
Tandem Queues ◽  
Tandem Queue ◽  
Service Times

We start from an earlier paper evaluating the overall sojourn time to derive the local sojourn time in stationary regime, in a single server tandem queue of (m+1) stages with renewal input. The successive service times of a customer may or may not be mutually dependent, and are governed by a general distribution which may be different at each sage.

A service model in which the server is required to search for customers

1984 ◽  
Vol 21 (01) ◽  
pp. 157-166 ◽  
Author(s):  
Marcel F. Neuts ◽  
M. F. Ramalhoto
Keyword(s):  
Poisson Process ◽  
Numerical Computation ◽  
Probability Distributions ◽  
General Distribution ◽  
Search Process ◽  
Single Server ◽  
Stationary Probability ◽  
Service Model ◽  
Service Times ◽  
Number Of Customers

Customers enter a pool according to a Poisson process and wait there to be found and processed by a single server. The service times of successive items are independent and have a common general distribution. Successive services are separated by seek phases during which the server searches for the next customer. The search process is Markovian and the probability of locating a customer in (t, t + dt) is proportional to the number of customers in the pool at time t. Various stationary probability distributions for this model are obtained in explicit forms well-suited for numerical computation. Under the assumption of exponential service times, corresponding results are obtained for the case where customers may escape from the pool.

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.

scholarly journals SRPT Scheduling Discipline in Many-Server Queues with Impatient Customers

2021 ◽  
Author(s):  
Jing Dong ◽  
Rouba Ibrahim
Keyword(s):  
Priority Queue ◽  
System Throughput ◽  
Single Server ◽  
Impatient Customers ◽  
Scheduling Policy ◽  
Multiserver Queues ◽  
Many Server Queues ◽  
Service Times ◽  
The Many ◽  
Queues With Abandonment

The shortest-remaining-processing-time (SRPT) scheduling policy has been extensively studied, for more than 50 years, in single-server queues with infinitely patient jobs. Yet, much less is known about its performance in multiserver queues. In this paper, we present the first theoretical analysis of SRPT in multiserver queues with abandonment. In particular, we consider the [Formula: see text] queue and demonstrate that, in the many-sever overloaded regime, performance in the SRPT queue is equivalent, asymptotically in steady state, to a preemptive two-class priority queue where customers with short service times (below a threshold) are served without wait, and customers with long service times (above a threshold) eventually abandon without service. We prove that the SRPT discipline maximizes, asymptotically, the system throughput, among all scheduling disciplines. We also compare the performance of the SRPT policy to blind policies and study the effects of the patience-time and service-time distributions. This paper was accepted by Baris Ata, stochastic models & simulation.

On a tandem queueing model with identical service times at both counters, I

1979 ◽  
Vol 11 (3) ◽  
pp. 616-643 ◽  
Author(s):  
O. J. Boxma
Keyword(s):  
Waiting Times ◽  
Sufficient Conditions ◽  
Complete Analysis ◽  
Single Server ◽  
Stationary Distributions ◽  
In Series ◽  
Queues In Series ◽  
Service Times ◽  
Necessary And Sufficient ◽  
Insight Into

This paper considers a queueing system consisting of two single-server queues in series, in which the service times of an arbitrary customer at both queues are identical. Customers arrive at the first queue according to a Poisson process.Of this model, which is of importance in modern network design, a rather complete analysis will be given. The results include necessary and sufficient conditions for stationarity of the tandem system, expressions for the joint stationary distributions of the actual waiting times at both queues and of the virtual waiting times at both queues, and explicit expressions (i.e., not in transform form) for the stationary distributions of the sojourn times and of the actual and virtual waiting times at the second queue.In Part II (pp. 644–659) these results will be used to obtain asymptotic and numerical results, which will provide more insight into the general phenomenon of tandem queueing with correlated service times at the consecutive queues.

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 M/G/1 queue with negative customers

1996 ◽  
Vol 28 (02) ◽  
pp. 540-566 ◽  
Author(s):  
Peter G. Harrison ◽  
Edwige Pitel
Keyword(s):  
Iterative Solution ◽  
Single Server ◽  
Negative Customers ◽  
Poisson Arrival ◽  
First Case ◽  
Full Study ◽  
Service Times ◽  
The Stability ◽  
The One ◽  
Iterative Solution Method

We derive expressions for the generating function of the equilibrium queue length probability distribution in a single server queue with general service times and independent Poisson arrival streams of both ordinary, positive customers and negative customers which eliminate a positive customer if present. For the case of first come first served queueing discipline for the positive customers, we compare the killing strategies in which either the last customer in the queue or the one in service is removed by a negative customer. We then consider preemptive-restart with resampling last come first served queueing discipline for the positive customers, combined with the elimination of the customer in service by a negative customer—the case of elimination of the last customer yields an analysis similar to first come first served discipline for positive customers. The results show different generating functions in contrast to the case where service times are exponentially distributed. This is also reflected in the stability conditions. Incidently, this leads to a full study of the preemptive-restart with resampling last come first served case without negative customers. Finally, approaches to solving the Fredholm integral equation of the first kind which arises, for instance, in the first case are considered as well as an alternative iterative solution method.

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