Sojourn times in single-server queues by negative customers

1993 ◽  
Vol 30 (4) ◽  
pp. 943-963 ◽  
Author(s):  
P. G. Harrison ◽  
E. Pitel
Keyword(s):  
Laplace Transform ◽  
Single Server ◽  
Processor Sharing ◽  
Single Server Queue ◽  
Negative Customers ◽  
Mean Values ◽  
Poisson Arrival ◽  
Server Queue ◽  
The Laplace Transform ◽  
Time Density

We derive expressions for the Laplace transform of the sojourn time density in a single-server queue with exponential service times and independent Poisson arrival streams of both ordinary, positive customers and negative customers which eliminate a positive customer if present. We compare first-come first-served and last-come first-served queueing disciplines for the positive customers, combined with elimination of the last customer in the queue or the customer in service by a negative customer. We also derive the corresponding result for processor-sharing discipline with random elimination. The results show differences not only in the Laplace transforms but also in the means of the distributions, in contrast to the case where there are no negative customers. The various combinations of queueing discipline and elimination strategy are ranked with respect to these mean values.

Sojourn times in single-server queues by negative customers

1993 ◽  
Vol 30 (04) ◽  
pp. 943-963
Author(s):  
P. G. Harrison ◽  
E. Pitel
Keyword(s):  
Laplace Transform ◽  
Single Server ◽  
Processor Sharing ◽  
Single Server Queue ◽  
Negative Customers ◽  
Mean Values ◽  
Poisson Arrival ◽  
Server Queue ◽  
The Laplace Transform ◽  
Time Density

We derive expressions for the Laplace transform of the sojourn time density in a single-server queue with exponential service times and independent Poisson arrival streams of both ordinary, positive customers and negative customers which eliminate a positive customer if present. We compare first-come first-served and last-come first-served queueing disciplines for the positive customers, combined with elimination of the last customer in the queue or the customer in service by a negative customer. We also derive the corresponding result for processor-sharing discipline with random elimination. The results show differences not only in the Laplace transforms but also in the means of the distributions, in contrast to the case where there are no negative customers. The various combinations of queueing discipline and elimination strategy are ranked with respect to these mean values.

A single server queue with gated processor-sharing discipline

1989 ◽  
Vol 4 (3) ◽  
pp. 249-261 ◽  
Author(s):  
Kiran M. Rege ◽  
Bhaskar Sengupta
Keyword(s):  
Single Server ◽  
Processor Sharing ◽  
Single Server Queue ◽  
Server Queue

Equilibrium Strategies for Processor Sharing and Random Queues with Relative Priorities

1997 ◽  
Vol 11 (4) ◽  
pp. 403-412 ◽  
Author(s):  
Moshe Haviv ◽  
Jan van der Wal
Keyword(s):  
Nash Equilibrium ◽  
Equilibrium Price ◽  
Single Server ◽  
Processor Sharing ◽  
Single Server Queue ◽  
Relative Priority ◽  
Equilibrium Strategies ◽  
Service Disciplines ◽  
Server Queue

We consider a memoryless single-server queue in which users can purchase relative priority so as to reduce their expected waiting costs, which are linear with time. Relative priority is given in proportion to a price paid by customers present in the system. For two service disciplines, (weighted) processor sharing and (weighted) random entrance, we find the unique pure and symmetric Nash equilibrium price paid by the customers.

scholarly journals A FLUID LIMIT FOR PROCESSOR-SHARING QUEUES WEIGHTED BY FUNCTIONS OF REMAINING AMOUNTS OF SERVICE

2019 ◽  
pp. 1-8
Author(s):  
Yingdong Lu
Keyword(s):  
Single Server ◽  
Processor Sharing ◽  
Single Server Queue ◽  
Fluid Limit ◽  
Scheduling Policy ◽  
Server Queue ◽  
Processor Sharing Queues

Abstract We study a single server queue under a processor-sharing type of scheduling policy, where the weights for determining the sharing are given by functions of each job's remaining service (processing) amount, and obtain a fluid limit for the scaled measure-valued system descriptors.

Single-Server Queue System of Shuttle Bus Performance: Federal University of Technology Akure as Case Study

2019 ◽  
Vol 5 (3) ◽  
pp. 9-14
Author(s):  
Sidiq Okwudili Ben
Keyword(s):  
Laplace Transform ◽  
Poisson Process ◽  
Service Rate ◽  
Single Server ◽  
Single Server Queue ◽  
Queue System ◽  
University Of Technology ◽  
Server Queue

This study has examined the performance of University transport bus shuttle based on utilization using a Single-server queue system which occur if arrival and service rate is Poisson distributed (single queue) (M/M/1) queue. In the methodology, Single-server queue system was modelled based on Poisson Process with the introduction of Laplace Transform. It is concluded that the performance of University transport bus shuttle is 96.6 percent which indicates a very good performance such that the supply of shuttle bus in FUTA is capable of meeting the demand.

On queues with periodic inputs

1989 ◽  
Vol 26 (02) ◽  
pp. 381-389 ◽  
Author(s):  
Nicholas Bambos ◽  
Jean Walrand
Keyword(s):  
Limit Theorems ◽  
Single Server ◽  
Single Server Queue ◽  
Input Process ◽  
Poisson Arrival ◽  
Server Queue ◽  
Asymptotically Periodic ◽  
Waiting Time Process ◽  
Periodic Inputs ◽  
Networks Of Queues

We consider a single-server queue with a periodic and ergodic input. It is shown that if the traffic intensity is less than 1, then the waiting time process is asymptotically periodic. Limit theorems associated with the asymptotic behavior of the queue are also proven. The results are then extended to acyclic networks of queues with periodic inputs. Particular cases of these results had been previously obtained for a single queue with periodic Poisson arrival input process and with independent and identically distributed service times.

scholarly journals Stationary queue length of a single-server queue with negative arrivals and nonexponential service time distributions

2018 ◽  
Vol 189 ◽  
pp. 02006 ◽  
Author(s):  
S K Koh ◽  
C H Chin ◽  
Y F Tan ◽  
L E Teoh ◽  
A H Pooi ◽  
...  
Keyword(s):  
Service Time ◽  
Queue Length ◽  
Queueing Systems ◽  
Length Distribution ◽  
Single Server ◽  
Service Time Distribution ◽  
Single Server Queue ◽  
Negative Customers ◽  
Stationary Queue Length ◽  
Server Queue

In this paper, a single-server queue with negative customers is considered. The arrival of a negative customer will remove one positive customer that is being served, if any is present. An alternative approach will be introduced to derive a set of equations which will be solved to obtain the stationary queue length distribution. We assume that the service time distribution tends to a constant asymptotic rate when time t goes to infinity. This assumption will allow for finding the stationary queue length of queueing systems with non-exponential service time distributions. Numerical examples for gamma distributed service time with fractional value of shape parameter will be presented in which the steady-state distribution of queue length with such service time distributions may not be easily computed by most of the existing analytical methods.

The total waiting time in a busy period of a stable single-server queue, II

1969 ◽  
Vol 6 (3) ◽  
pp. 565-572 ◽  
Author(s):  
D. J. Daley ◽  
D. R. Jacobs
Keyword(s):  
Waiting Time ◽  
Busy Period ◽  
Bessel Functions ◽  
Arrival Process ◽  
Single Server ◽  
Single Server Queue ◽  
Common Distribution ◽  
Poisson Arrival ◽  
Server Queue ◽  
Common Distribution Function

This paper is a continuation of Daley (1969), referred to as (I), whose notation and numbering is continued here. We shall indicate various approaches to the study of the total waiting time in a busy period2 of a stable single-server queue with a Poisson arrival process at rate λ, and service times independently distributed with common distribution function (d.f.) B(·). Let X'i denote3 the total waiting time in a busy period which starts at an epoch when there are i (≧ 1) customers in the system (to be precise, the service of one customer is just starting and the remaining i − 1 customers are waiting for service). We shall find the first two moments of X'i, prove its asymptotic normality for i → ∞ when B(·) has finite second moment, and exhibit the Laplace-Stieltjes transform of X'i in M/M/1 as the ratio of two Bessel functions.

scholarly journals Geo/Geo/1/N Queue with In-Immune and Immune Service Killing Discipline

2012 ◽  
Vol 23 (1) ◽  
pp. 129-148
Author(s):  
Madhu Jain Madhu Jain
Keyword(s):  
Performance Measures ◽  
Generating Functions ◽  
Relaxation Method ◽  
Single Server ◽  
Finite Capacity ◽  
Single Server Queue ◽  
Stationary Probability Distribution ◽  
Negative Customers ◽  
Server Queue ◽  
Successive Over Relaxation

The present investigation studies a discrete time single server queue with both positive and negative arrival streams in accordance with removal of the customer from the end (RCE)-in immune and immune service killing policy. This study is a generalization of the queue with negative customers, wherein only positive customers need a service and negative customers arriving to the system can kill the already present positive customers from any where in the queue, otherwise get lost. The concept of both in-immune and immune service killing are taken into consideration. According to the in-immune killing policy, the negative customer is allowed to kill the most recent positive customer inspite of whether it is in service or not, while the immune service killing discipline suggests that the customer currently being served is immune from killing by the negative arrival. We analyze a queue with geometric arrivals of both positive and negative customers for a finite capacity system. The stationary probability distribution and other performance measures are derived in terms of the generating functions. The results so obtained are validated by the numerical method based on successive over relaxation method (SOR). We have also employed the neurro fuzzy approach for exhibiting the approximate results for various performance measures.

On queues with periodic inputs

1989 ◽  
Vol 26 (2) ◽  
pp. 381-389 ◽  
Author(s):  
Nicholas Bambos ◽  
Jean Walrand
Keyword(s):  
Limit Theorems ◽  
Single Server ◽  
Single Server Queue ◽  
Input Process ◽  
Poisson Arrival ◽  
Server Queue ◽  
Asymptotically Periodic ◽  
Waiting Time Process ◽  
Periodic Inputs ◽  
Networks Of Queues

We consider a single-server queue with a periodic and ergodic input. It is shown that if the traffic intensity is less than 1, then the waiting time process is asymptotically periodic. Limit theorems associated with the asymptotic behavior of the queue are also proven. The results are then extended to acyclic networks of queues with periodic inputs. Particular cases of these results had been previously obtained for a single queue with periodic Poisson arrival input process and with independent and identically distributed service times.

Sign in / Sign up

Export Citation Format

Share Document