Comparisons of Service Disciplines in a Queueing System with Delay Dependent Customer Behaviour

1982 ◽  
pp. 269-304 ◽  
Author(s):  
Bharat T. Doshi ◽  
Edward H. Lipper
Keyword(s):  
Queueing System ◽  
System With Delay ◽  
Customer Behaviour ◽  
Service Disciplines ◽  
Delay Dependent

On extremal service disciplines in single-stage queueing systems

1990 ◽  
Vol 27 (02) ◽  
pp. 409-416 ◽  
Author(s):  
Rhonda Righter ◽  
J. George Shanthikumar ◽  
Genji Yamazaki
Keyword(s):  
Service Time ◽  
Sojourn Time ◽  
Queueing System ◽  
Residual Life ◽  
Queueing Systems ◽  
Mean Residual Life ◽  
Service Discipline ◽  
Service Time Distribution ◽  
Service Disciplines ◽  
Number Of Customers

It is shown that among all work-conserving service disciplines that are independent of the future history, the first-come-first-served (FCFS) service discipline minimizes [maximizes] the average sojourn time in a G/GI/1 queueing system with new better [worse] than used in expectation (NBUE[NWUE]) service time distribution. We prove this result using a new basic identity of G/GI/1 queues that may be of independent interest. Using a relationship between the workload and the number of customers in the system with different lengths of attained service it is shown that the average sojourn time is minimized [maximized] by the least-attained-service time (LAST) service discipline when the service time has the decreasing [increasing] mean residual life (DMRL[IMRL]) property.

On extremal service disciplines in single-stage queueing systems

1990 ◽  
Vol 27 (2) ◽  
pp. 409-416 ◽  
Author(s):  
Rhonda Righter ◽  
J. George Shanthikumar ◽  
Genji Yamazaki
Keyword(s):  
Service Time ◽  
Sojourn Time ◽  
Queueing System ◽  
Residual Life ◽  
Queueing Systems ◽  
Mean Residual Life ◽  
Service Discipline ◽  
Service Time Distribution ◽  
Service Disciplines ◽  
Number Of Customers

It is shown that among all work-conserving service disciplines that are independent of the future history, the first-come-first-served (FCFS) service discipline minimizes [maximizes] the average sojourn time in a G/GI/1 queueing system with new better [worse] than used in expectation (NBUE[NWUE]) service time distribution. We prove this result using a new basic identity of G/GI/1 queues that may be of independent interest. Using a relationship between the workload and the number of customers in the system with different lengths of attained service it is shown that the average sojourn time is minimized [maximized] by the least-attained-service time (LAST) service discipline when the service time has the decreasing [increasing] mean residual life (DMRL[IMRL]) property.

On the mean sojourn time of jobs in queues by general service disciplines

1994 ◽  
Vol 26 (02) ◽  
pp. 516-538
Author(s):  
Gunter Ritter
Keyword(s):  
Ergodic Theorem ◽  
Sojourn Time ◽  
Queueing System ◽  
Input Stream ◽  
Sample Mean ◽  
Batch Arrivals ◽  
Processing Times ◽  
Service Disciplines ◽  
The Mean ◽  
General Service

Existence and finiteness of the sample-mean limit of sojourn times of jobs in a queueing system are investigated. The queueing system operates under rather general multiprocessor disciplines allowing job classes and priorities. The input stream of jobs consisting of job classes and interarrival and processing times is stationary and ergodic and may contain batch arrivals. Existence of the sample-mean limit is proved by means of the superadditive ergodic theorem, and its finiteness is controlled by uniform mixing of the input stream.

On Queues with Priority Determined by Feedback

2018 ◽  
Vol 70 (1) ◽  
pp. 33-56 ◽  
Author(s):  
A. Krishnamoorthy ◽  
A. S. Manjunath
Keyword(s):  
Queueing System ◽  
Text Line ◽  
Waiting Time Distribution ◽  
Bernoulli Process ◽  
Left Behind ◽  
Service Disciplines ◽  
Phase Type ◽  
Waiting Line ◽  
Special Case ◽  
Priority Queueing

Customers arrive to a two-priority queueing system according to a marked Poisson process. Both waiting rooms have infinite capacity. Customers are served one at a time according to FIFO discipline on priority basis: those in waiting line 1([Formula: see text]) are given priority over the ones in line 2([Formula: see text]). The service time is class-dependent phase type. After completion of service, high priority ([Formula: see text]) customers may feed back for service according to a Bernoulli process. Feed back customers are sent to the low priority ([Formula: see text]) queue. When at a service completion epoch of a [Formula: see text] customer, if there is none left behind in [Formula: see text] line, then the server goes to serve [Formula: see text] class. For the two-priority queueing system, we assume that [Formula: see text] customers are not allowed an additional feed back. Both preemptive and non-preemptive service disciplines are analysed. Waiting time distribution of both type of customers are derived. As a special case, the situation where there is no external entry to the [Formula: see text] line is discussed.

scholarly journals The Effect of a Service Experience Cost on a Queueing System

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Xuelu Zhang ◽  
Qing Ma
Keyword(s):  
Social Welfare ◽  
Queueing System ◽  
Numerical Results ◽  
Equilibrium Strategy ◽  
Service Experience ◽  
Customer Behaviour

In this work, the authors consider the effect of a service experience cost (SE cost) on customer behaviour in the M/M/1 queueing system. Based on customer individual equilibrium strategy, social welfare is also analyzed in unobservable and observable cases. The SE cost decreases the equilibrium joining probability and social welfare in an unobservable case. However, there might exist multiple individual equilibrium thresholds in an observable case. Furthermore, numerical results show that the SE cost can be used as a feasible policy to make an incentive for customers and regulate the system for improved social welfare in some scenarios.

On the mean sojourn time of jobs in queues by general service disciplines

1994 ◽  
Vol 26 (2) ◽  
pp. 516-538 ◽  
Author(s):  
Gunter Ritter
Keyword(s):  
Ergodic Theorem ◽  
Sojourn Time ◽  
Queueing System ◽  
Input Stream ◽  
Sample Mean ◽  
Batch Arrivals ◽  
Processing Times ◽  
Service Disciplines ◽  
The Mean ◽  
General Service

Existence and finiteness of the sample-mean limit of sojourn times of jobs in a queueing system are investigated. The queueing system operates under rather general multiprocessor disciplines allowing job classes and priorities. The input stream of jobs consisting of job classes and interarrival and processing times is stationary and ergodic and may contain batch arrivals. Existence of the sample-mean limit is proved by means of the superadditive ergodic theorem, and its finiteness is controlled by uniform mixing of the input stream.

scholarly journals The Lyapunov-Razumikhin theorem for the conformable fractional system with delay

2021 ◽  
Vol 7 (3) ◽  
pp. 4795-4802
Author(s):  
Narongrit Kaewbanjak ◽  
◽  
Watcharin Chartbupapan ◽  
Kamsing Nonlaopon ◽  
Kanit Mukdasai ◽  
...  
Keyword(s):  
Asymptotic Stability ◽  
Lyapunov Functional ◽  
Stability Theorem ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Uniform Asymptotic Stability ◽  
Razumikhin Theorem ◽  
System With Delay ◽  
Fractional System ◽  
Delay Dependent

<abstract><p>This paper explicates the Razumikhin-type uniform stability and a uniform asymptotic stability theorem for the conformable fractional system with delay. Based on a Razumikhin-Lyapunov functional and some inequalities, a delay-dependent asymptotic stability criterion is in the term of a linear matrix inequality (LMI) for the conformable fractional linear system with delay. Moreover, an application of our theorem is illustrated via a numerical example.</p></abstract>

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