A SINGLE-SERVER QUEUEING SYSTEM WITH LIFO SERVICE, PROBABILISTIC PRIORITY, BATCH POISSON ARRIVALS, AND BACKGROUND CUSTOMERS

2020 ◽  
Keyword(s):  
Queueing System ◽  
Single Server ◽  
Poisson Arrivals

scholarly journals MX/G/1 Vacation Queueing System with Two Types of Repair facilities and Server Timeout

2019 ◽  
Vol 8 (9) ◽  
pp. 2040-2043
Keyword(s):  
Size Distribution ◽  
Exponential Distribution ◽  
Service Time ◽  
Queueing System ◽  
Batch Size ◽  
Single Server ◽  
Poisson Arrivals ◽  
Server Failure ◽  
System Length ◽  
General Service

We consider a single server vacation queue with two types of repair facilities and server timeout. Here customers are in compound Poisson arrivals with general service time and the lifetime of the server follows an exponential distribution. The server find if the system is empty, then he will wait until the time ‘c’. At this time if no one customer arrives into the system, then the server takes vacation otherwise the server commence the service to the arrived customers exhaustively. If the system had broken down immediately, it is sent for repair. Here server failure can be rectified in two case types of repair facilities, case1, as failure happens during customer being served willstays in service facility with a probability of 1-q to complete the remaining service and in case2 it opts for new service also who joins in the head of the queue with probability q. Obtained an expression for the expected system length for different batch size distribution and also numerical results are shown

scholarly journals A transient solution to an M/M/1 queue: a simple approach

1987 ◽  
Vol 19 (04) ◽  
pp. 997-998 ◽  
Author(s):  
P. R. Parthasarathy
Keyword(s):  
Queueing System ◽  
Simple Approach ◽  
Time Dependent ◽  
Single Server ◽  
Transient Solution ◽  
Poisson Arrivals ◽  
Service Times ◽  
Time Dependent Solution

A time-dependent solution for the number in a single-server queueing system with Poisson arrivals and exponential service times is derived in a direct way.

Some applications of the theory of infinite capacity service systems to a single server system with linearly state dependent service

1971 ◽  
Vol 8 (01) ◽  
pp. 202-207
Author(s):  
B. W. Conolly
Keyword(s):  
Queueing System ◽  
Service Systems ◽  
Single Server ◽  
Simple Manner ◽  
State Dependent ◽  
Poisson Arrivals ◽  
Negative Exponential ◽  
Server System

Summary A certain single server queueing system with negative exponential service with mean rate nμ, when the system contains n customers, and Poisson arrivals, is formally equivalent to the infinite capacity system M/M/∞. This equivalence is exploited to yield in a very simple manner results for the single server system which were previously obtained by difficult analysis (see Hadidi (1969)).

A bivariate Poisson queueing process that is not infinitely divisible

1972 ◽  
Vol 72 (3) ◽  
pp. 449-450 ◽  
Author(s):  
D. J. Daley
Keyword(s):  
Poisson Process ◽  
Point Process ◽  
Queueing System ◽  
Poisson Processes ◽  
Single Server ◽  
Infinitely Divisible ◽  
Queueing Process ◽  
Input And Output ◽  
Poisson Arrivals ◽  
Bivariate Poisson Process

We are using the term ‘bivariate Poisson process’ to describe a bivariate point process (N1(.), N2(.)) whose components (or, marginal processes) are Poisson processes. In this we are following Milne (2) who amongst his examples cites the case where N1(.) and N2(.) refer to the input and output processes respectively of the M/G/∈ queueing system. Such a bivariate point process is infinitely divisible. We shall now show that in a stationary M/M/1 queueing system (i.e. Poisson arrivals at rate λ, exponential service at rate µ > λ, single-server) a similar identification of (N1(.), N2(.)) yields a bivariate Poisson process that is not infinitely divisible.

Assigning Priorities (or Not) in Service Systems with Nonlinear Waiting Costs

2021 ◽  
Author(s):  
Huiyin Ouyang ◽  
Nilay Taník Argon ◽  
Serhan Ziya
Keyword(s):  
Service Time ◽  
Queueing System ◽  
Numerical Study ◽  
Arrival Rate ◽  
The Other ◽  
Cost Functions ◽  
Single Server ◽  
Dominant Type ◽  
Fixed Priority ◽  
Poisson Arrivals

For a queueing system with multiple customer types differing in service-time distributions and waiting costs, it is well known that the cµ-rule is optimal if costs for waiting are incurred linearly with time. In this paper, we seek to identify policies that minimize the long-run average cost under nonlinear waiting cost functions within the set of fixed priority policies that only use the type identities of customers independently of the system state. For a single-server queueing system with Poisson arrivals and two or more customer types, we first show that some form of the cµ-rule holds with the caveat that the indices are complex, depending on the arrival rate, higher moments of service time, and proportions of customer types. Under quadratic cost functions, we provide a set of conditions that determine whether to give priority to one type over the other or not to give priority but serve them according to first-come, first-served (FCFS). These conditions lead to useful insights into when strict (and fixed) priority policies should be preferred over FCFS and when they should be avoided. For example, we find that, when traffic is heavy, service times are highly variable, and the customer types are not heterogenous, so then prioritizing one type over the other (especially a proportionally dominant type) would be worse than not assigning any priority. By means of a numerical study, we generate further insights into more specific conditions under which fixed priority policies can be considered as an alternative to FCFS. This paper was accepted by Baris Ata, stochastic models and simulation.

On the quasi-stationary distribution of the virtual waiting time in queues with Poisson arrivals

1971 ◽  
Vol 8 (3) ◽  
pp. 494-507 ◽  
Author(s):  
E. K. Kyprianou
Keyword(s):  
Waiting Time ◽  
Busy Period ◽  
Queueing System ◽  
Random Variable ◽  
Single Server ◽  
Virtual Waiting Time ◽  
Waiting Time Process ◽  
Poisson Arrivals ◽  
Image Position ◽  
Quasi Stationary Distribution

We consider a single server queueing system M/G/1 in which customers arrive in a Poisson process with mean λt, and the service time has distribution dB(t), 0 < t < ∞. Let W(t) be the virtual waiting time process, i.e., the time that a potential customer arriving at the queueing system at time t would have to wait before beginning his service. We also let the random variable denote the first busy period initiated by a waiting time u at time t = 0.

Some applications of the theory of infinite capacity service systems to a single server system with linearly state dependent service

1971 ◽  
Vol 8 (1) ◽  
pp. 202-207 ◽  
Author(s):  
B. W. Conolly
Keyword(s):  
Queueing System ◽  
Service Systems ◽  
Single Server ◽  
Simple Manner ◽  
State Dependent ◽  
Poisson Arrivals ◽  
Negative Exponential ◽  
Server System

SummaryA certain single server queueing system with negative exponential service with mean rate nμ, when the system contains n customers, and Poisson arrivals, is formally equivalent to the infinite capacity system M/M/∞. This equivalence is exploited to yield in a very simple manner results for the single server system which were previously obtained by difficult analysis (see Hadidi (1969)).

On the quasi-stationary distribution of the virtual waiting time in queues with Poisson arrivals

1971 ◽  
Vol 8 (03) ◽  
pp. 494-507 ◽  
Author(s):  
E. K. Kyprianou
Keyword(s):  
Waiting Time ◽  
Busy Period ◽  
Queueing System ◽  
Random Variable ◽  
Single Server ◽  
Virtual Waiting Time ◽  
Waiting Time Process ◽  
Poisson Arrivals ◽  
Image Position ◽  
Quasi Stationary Distribution

We consider a single server queueing system M/G/1 in which customers arrive in a Poisson process with mean λt, and the service time has distribution dB(t), 0 &lt; t &lt; ∞. Let W(t) be the virtual waiting time process, i.e., the time that a potential customer arriving at the queueing system at time t would have to wait before beginning his service. We also let the random variable denote the first busy period initiated by a waiting time u at time t = 0.

scholarly journals A transient solution to an M/M/1 queue: a simple approach

1987 ◽  
Vol 19 (4) ◽  
pp. 997-998 ◽  
Author(s):  
P. R. Parthasarathy
Keyword(s):  
Queueing System ◽  
Simple Approach ◽  
Time Dependent ◽  
Single Server ◽  
Transient Solution ◽  
Poisson Arrivals ◽  
Service Times ◽  
Time Dependent Solution

A time-dependent solution for the number in a single-server queueing system with Poisson arrivals and exponential service times is derived in a direct way.

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