Sensitivity analysis for stationary and ergodic queues

1992 ◽  
Vol 24 (3) ◽  
pp. 738-750 ◽  
Author(s):  
P. Konstantopoulos ◽  
Michael A. Zazanis
Keyword(s):  
Sensitivity Analysis ◽  
Steady State ◽  
Performance Measures ◽  
Perturbation Analysis ◽  
Service Process ◽  
Single Server ◽  
Stationary Version ◽  
Major Interest ◽  
Regenerative Approach ◽  
Steady State Performance

Starting with some mild assumptions on the parametrization of the service process, perturbation analysis (PA) estimates are obtained for stationary and ergodic single-server queues. Besides relaxing the stochastic assumptions, our approach solves some problems associated with the traditional regenerative approach taken in most of the previous work in this area. First, it avoids problems caused by perturbations interfering with the regenerative structure of the system. Second, given that the major interest is in steady-state performance measures, it examines directly the stationary version of the system, instead of considering performance measures expressed as Cesaro limits. Finally, it provides new estimators for general (possibly discontinuous) functions of the workload and other steady-state quantities.

Sensitivity analysis for stationary and ergodic queues

1992 ◽  
Vol 24 (03) ◽  
pp. 738-750 ◽  
Author(s):  
P. Konstantopoulos ◽  
Michael A. Zazanis
Keyword(s):  
Sensitivity Analysis ◽  
Steady State ◽  
Performance Measures ◽  
Perturbation Analysis ◽  
Service Process ◽  
Single Server ◽  
Stationary Version ◽  
Major Interest ◽  
Regenerative Approach ◽  
Steady State Performance

Starting with some mild assumptions on the parametrization of the service process, perturbation analysis (PA) estimates are obtained for stationary and ergodic single-server queues. Besides relaxing the stochastic assumptions, our approach solves some problems associated with the traditional regenerative approach taken in most of the previous work in this area. First, it avoids problems caused by perturbations interfering with the regenerative structure of the system. Second, given that the major interest is in steady-state performance measures, it examines directly the stationary version of the system, instead of considering performance measures expressed as Cesaro limits. Finally, it provides new estimators for general (possibly discontinuous) functions of the workload and other steady-state quantities.

scholarly journals Modelling customers’ impatience with discouraged arrival and retention of reneging

2021 ◽  
Vol 31 (3) ◽  
Author(s):  
Pallabi Medhi
Keyword(s):  
Sensitivity Analysis ◽  
Steady State ◽  
Performance Measures ◽  
Generating Functions ◽  
Stochastic Modelling ◽  
Steady State Solution ◽  
Single Server ◽  
Finite Buffer ◽  
System Parameters ◽  
Retention Of Reneged Customers

This paper presents stochastic modelling of a single server, finite buffer Markovian queuing system with discouraged arrivals, balking, reneging, and retention of reneged customers. Markov process is used to derive the steady-state solution of the model. Closed form expressions using probability generating functions (PGFs) are derived and presented for both classical and novel performance measures. In addition, a sensitivity analysis is carried out to study the effect of the system parameters on performance measures. A numerical problem is also presented to demonstrate the derived results and some design aspects.

A single server Markovian queuing system with limited buffer and reverse balking

2021 ◽  
Vol 12 (7) ◽  
pp. 1774-1784
Author(s):  
Girin Saikia ◽  
Amit Choudhury
Keyword(s):  
Steady State ◽  
Performance Measures ◽  
Mutual Fund ◽  
System Size ◽  
Queuing System ◽  
Single Server ◽  
Insurance Company ◽  
Number Of Customers ◽  
Steady State Probabilities

The phenomena are balking can be said to have been observed when a customer who has arrived into queuing system decides not to join it. Reverse balking is a particular type of balking wherein the probability that a customer will balk goes down as the system size goes up and vice versa. Such behavior can be observed in investment firms (insurance company, Mutual Fund Company, banks etc.). As the number of customers in the firm goes up, it creates trust among potential investors. Fewer customers would like to balk as the number of customers goes up. In this paper, we develop an M/M/1/k queuing system with reverse balking. The steady-state probabilities of the model are obtained and closed forms of expression of a number of performance measures are derived.

scholarly journals On Mx/(G1G2)/1/G(BS)/Vs vacation queue with two types of general heterogeneous service

2005 ◽  
Vol 2005 (3) ◽  
pp. 123-135 ◽  
Author(s):  
Kailash C. Madan ◽  
Z. R. Al-Rawi ◽  
Amjad D. Al-Nasser
Keyword(s):  
Steady State ◽  
Performance Measures ◽  
Waiting Time ◽  
Busy Period ◽  
Single Server ◽  
Queue Size ◽  
Single Vacation ◽  
The Mean ◽  
Expected Waiting Time ◽  
Heterogeneous Service

We analyze a batch arrival queue with a single server providing two kinds of general heterogeneous service. Just before his service starts, a customer may choose one of the services and as soon as a service (of any kind) gets completed, the server may take a vacation or may continue staying in the system. The vacation times are assumed to be general and the server vacations are based on Bernoulli schedules under a single vacation policy. We obtain explicit queue size distribution at a random epoch as well as at a departure epoch and also the mean busy period of the server under the steady state. In addition, some important performance measures such as the expected queue size and the expected waiting time of a customer are obtained. Further, some interesting particular cases are also discussed.

scholarly journals Loss Systems with Slow Retrials in the Halfin–Whitt Regime

2013 ◽  
Vol 45 (01) ◽  
pp. 274-294 ◽  
Author(s):  
F. Avram ◽  
A. J. E. M. Janssen ◽  
J. S. H. Van Leeuwaarden
Keyword(s):  
Steady State ◽  
Critical Load ◽  
Performance Measures ◽  
System Performance ◽  
Economies Of Scale ◽  
Blocking Probability ◽  
Loss System ◽  
Qed Regime ◽  
Loss Systems ◽  
Steady State Performance

The Halfin–Whitt regime, or the quality-and-efficiency-driven (QED) regime, for multiserver systems refers to a situation with many servers, a critical load, and yet favorable system performance. We apply this regime to the classical multiserver loss system with slow retrials. We derive nondegenerate limiting expressions for the main steady-state performance measures, including the retrial rate and the blocking probability. It is shown that the economies of scale associated with the QED regime persist for systems with retrials, although in situations when the load becomes extremely critical the retrials cause deteriorated performance. Most of our results are obtained by a detailed analysis of Cohen's equation that defines the retrial rate in an implicit way. The limiting expressions are established by studying prelimit behavior and exploiting the connection between Cohen's equation and Mills' ratio for the Gaussian and Poisson distributions.

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