scholarly journals A preemptive priority queue with a general bulk service rule

1986 ◽  
Vol 33 (2) ◽  
pp. 237-243 ◽  
Author(s):  
R. Sivasamy
Keyword(s):  
Queueing System ◽  
Priority Queue ◽  
Single Server ◽  
Preemptive Priority ◽  
Lower Priority ◽  
Bulk Service ◽  
Queue Lengths ◽  
The Mean ◽  
General Bulk Service Rule ◽  
Priority Queueing

In this paper a single server preemptive priority queueing system, consisting of two types of units, with unlimited Poisson inputs and exponential service time distributions, is studied. The higher priority units are served in batches according to a general bulk service rule and they have preemptive priority over lower priority units. Steady state queue length distributions, stability condition and the mean queue lengths are obtained.

scholarly journals From Exhaustive Vacation Queues to Preemptive Priority Queues with General Interarrival Times

2018 ◽  
Vol 28 (4) ◽  
pp. 695-704
Author(s):  
Dieter Fiems ◽  
Stijn De Vuyst
Keyword(s):  
Discrete Time ◽  
Queueing System ◽  
Queueing Systems ◽  
Probability Generating Function ◽  
Priority Queue ◽  
Preemptive Priority ◽  
Numerical Examples ◽  
Preemptive Resume ◽  
Completion Times ◽  
Priority Queueing

Abstract We consider the discrete-time G/GI/1 queueing system with multiple exhaustive vacations. By a transform approach, we obtain an expression for the probability generating function of the waiting time of customers in such a system. We then show that the results can be used to assess the performance of G/GI/1 queueing systems with server breakdowns as well as that of the low-priority queue of a preemptive MX+G/GI/1 priority queueing system. By calculating service completion times of low-priority customers, various preemptive breakdown/priority disciplines can be studied, including preemptive resume and preemptive repeat, as well as their combinations. We illustrate our approach with some numerical examples.

A Single Server Retrial Queueing System with Two Types of Batch Arrivals

2016 ◽  
pp. 55-70
Author(s):  
Kalyanaraman Rathinasabapathy
Keyword(s):  
Queueing System ◽  
Numerical Study ◽  
Priority Queue ◽  
Single Server ◽  
Type I ◽  
Type Ii ◽  
Operating Characteristics ◽  
Batch Arrivals ◽  
Retrial Queueing System ◽  
Retrial Queueing

A retrial queueing system with two types of batch arrivals is considered. The arrivals are called type I and type II customers. The type I customers arrive in batches of size k with probability c_k and type II customers arrive in batches of size k with probability d_k. Service time distributions are identical independent distributions and are different for both type of customers. If the arriving customers are blocked due to server being busy, type I customers are queued in a priority queue of infinity capacity whereas type II customers entered into retrial group in order to seek service again after a random amount of time. For this model the joint distribution of the number of customers in the priority queue and in the retrial group in closed form is obtained. Some particular models and operating characteristics are obtained. A numerical study is also carried out.

scholarly journals A Priority Queue with Many Customer Types, Correlated Arrivals and Changing Priorities

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1292
Author(s):  
Seokjun Lee ◽  
Sergei Dudin ◽  
Olga Dudina ◽  
Chesoong Kim ◽  
Valentina Klimenok
Keyword(s):  
Markov Chain ◽  
Waiting Time ◽  
Performance Indicators ◽  
Queueing System ◽  
Priority Queue ◽  
First Aid ◽  
Single Server ◽  
Finite Buffer ◽  
Impatient Customers ◽  
Arrival Times

A single-server queueing system with a finite buffer, several types of impatient customers, and non-preemptive priorities is analyzed. The initial priority of a customer can increase during its waiting time in the queue. The behavior of the system is described by a multi-dimensional Markov chain. The generator of this chain, having essential dependencies between the components, is derived and formulas for computation of the most important performance indicators of the system are presented. The dependence of some of these indicators on the capacity of the buffer space is illustrated. The profound effect of the phenomenon of correlation of successive inter-arrival times and variance of the service time is numerically demonstrated. Results can be used for the optimization of dispatching various types of customers in information transmission systems, emergency departments and first aid stations, perishable foods supply chains, etc.

A limit theorem for priority queues in heavy traffic

1973 ◽  
Vol 10 (04) ◽  
pp. 907-912 ◽  
Author(s):  
J. Michael Harrison
Keyword(s):  
Limit Theorem ◽  
Queueing System ◽  
Heavy Traffic ◽  
Critical Value ◽  
Single Server ◽  
Traffic Condition ◽  
Transient Distribution ◽  
Virtual Waiting Time ◽  
Waiting Time Process ◽  
Priority Queueing

A single server, two priority queueing system is studied under the heavy traffic condition where the system traffic intensity is either at or near its critical value. An approximation is developed for the transient distribution of the low priority customers' virtual waiting time process. This result is stated formally as a limit theorem involving a sequence of systems whose traffic intensities approach the critical value.

Transient Analysis of a Non-Preemptive Priority Queueing System

2018 ◽  
Vol 12 (3) ◽  
pp. 645-654
Author(s):  
V. S. S. Yadavalli ◽  
Diatha Krishna Sundar ◽  
Swaminathan Udayabaskaran ◽  
C. T. Dora Pravina
Keyword(s):  
Transient Analysis ◽  
Queueing System ◽  
Preemptive Priority ◽  
Priority Queueing

A limit theorem for priority queues in heavy traffic

1973 ◽  
Vol 10 (4) ◽  
pp. 907-912 ◽  
Author(s):  
J. Michael Harrison
Keyword(s):  
Limit Theorem ◽  
Queueing System ◽  
Heavy Traffic ◽  
Critical Value ◽  
Single Server ◽  
Traffic Condition ◽  
Transient Distribution ◽  
Virtual Waiting Time ◽  
Waiting Time Process ◽  
Priority Queueing

A single server, two priority queueing system is studied under the heavy traffic condition where the system traffic intensity is either at or near its critical value. An approximation is developed for the transient distribution of the low priority customers' virtual waiting time process. This result is stated formally as a limit theorem involving a sequence of systems whose traffic intensities approach the critical value.

scholarly journals Analysis of a Discrete-Time Queueing Model with Disasters

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3283
Author(s):  
Mustafa Demircioglu ◽  
Herwig Bruneel ◽  
Sabine Wittevrongel
Keyword(s):  
Discrete Time ◽  
Queueing System ◽  
Time Slot ◽  
Probability Distributions ◽  
Single Server ◽  
Bernoulli Process ◽  
Tail Probabilities ◽  
Mean Values ◽  
The Mean ◽  
The Impact

Queueing models with disasters can be used to evaluate the impact of a breakdown or a system reset in a service facility. In this paper, we consider a discrete-time single-server queueing system with general independent arrivals and general independent service times and we study the effect of the occurrence of disasters on the queueing behavior. Disasters occur independently from time slot to time slot according to a Bernoulli process and result in the simultaneous removal of all customers from the queueing system. General probability distributions are allowed for both the number of customer arrivals during a slot and the length of the service time of a customer (expressed in slots). Using a two-dimensional Markovian state description of the system, we obtain expressions for the probability, generating functions, the mean values, variances and tail probabilities of both the system content and the sojourn time of an arbitrary customer under a first-come-first-served policy. The customer loss probability due to a disaster occurrence is derived as well. Some numerical illustrations are given.

scholarly journals Probabilistic Decomposition Method on the ServerIndices of anMξ/G/1 Vacation Queue

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Renbin Liu
Keyword(s):  
Decomposition Method ◽  
Queueing System ◽  
Stochastic Order ◽  
Single Server ◽  
Production Facility ◽  
Performance Indices ◽  
Illustrative Purpose ◽  
Novel Method ◽  
The Mean ◽  
Convolution Equations

This paper develops a probabilistic decomposition method for anMξ/G/1 repairable queueing system with multiple vacations, in which the customers who arrive during server vacations enter the system with probabilityp. Such a novel method is used to analyze the main performance indices of the server, such as the unavailability and the mean failure number during(0,t]. It is derived that the structures of server indices are two convolution equations. Further, comparisons with existing methods indicate that our method is effective and applicable for studying server performances in single-serverMξ/G/1 vacation queues and their complex variants. Finally, a stochastic order and production system with a multipurpose production facility is numerically presented for illustrative purpose.

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