Analysis of Two Phases Queue With Vacations and Breakdowns Under T-Policy

2019 ◽  
pp. 13-31
Author(s):  
Khalid Alnowibet ◽  
Lotfi Tadj
Keyword(s):  
Markov Chain ◽  
Steady State ◽  
Performance Measures ◽  
Threshold Level ◽  
System Size ◽  
State System ◽  
Markov Chain Approach ◽  
Optimal Value ◽  
Two Phases ◽  
Random Breakdowns

The service system considered in this chapter is characterized by an unreliable server. Random breakdowns occur on the server and the repair may not be immediate. The authors assume the possibility that the server may take a vacation at the end of a given service completion. The server resumes operation according to T-policy to check if enough customers have arrived while he was away. The actual service of any arrival takes place in two consecutive phases. Both service phases are independent of each other. A Markov chain approach is used to obtain the steady state system size probabilities and different performance measures. The optimal value of the threshold level is obtained analytically.

Analysis of Two Phases Queue With Vacations and Breakdowns Under T-Policy

2018 ◽  
pp. 1570-1583
Author(s):  
Khalid Alnowibet ◽  
Lotfi Tadj
Keyword(s):  
Markov Chain ◽  
Steady State ◽  
Performance Measures ◽  
Threshold Level ◽  
System Size ◽  
State System ◽  
Markov Chain Approach ◽  
Optimal Value ◽  
Two Phases ◽  
Random Breakdowns

The service system considered in this chapter is characterized by an unreliable server. Random breakdowns occur on the server and the repair may not be immediate. We assume the possibility that the server may take a vacation at the end of a given service completion. The server resumes operation according to T-policy to check if enough customers have arrived while he was away. The actual service of any arrival takes place in two consecutive phases. Both service phases are independent of each other. A Markov chain approach is used to obtain the steady state system size probabilities and different performance measures. The optimal value of the threshold level is obtained analytically.

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.

Performance Analysis of a Markovian Queuing System with Reneging and Retention of Reneged Customers

2017 ◽  
pp. 686-694
Author(s):  
Rakesh Kumar
Keyword(s):  
Steady State ◽  
Performance Measures ◽  
Cost Model ◽  
Customer Retention ◽  
System Size ◽  
Retention Mechanism ◽  
Queuing System ◽  
System Capacity ◽  
Service Rate ◽  
Retention Of Reneged Customers

In this chapter a finite capacity single server Markovian queuing system with reneging and retention of reneged customers is considered. It is envisaged that a reneging customer may be convinced to stay for his service if some customer retention mechanism is employed. Thus, there is a probability that a reneging customer may be retained. Steady-state balance equations of the model are derived using Markov chain theory. The steady-state probabilities of system size are obtained explicitly by using iterative method. The performance measures like expected system size, expected rate of reneging, and expected rate of retention are obtained. The effect of probability of retaining a reneging customer on the performance measures is studied. The economic analysis of the model is performed by developing a cost model. The optimum service rate and optimum system capacity are obtained using classical optimization and pattern search techniques. The optimization carried out helps to identify the optimum customer retention strategy from among many.

scholarly journals The Steady-State System Size Distribution for a Modified D-Policy Geo/G/1 Queueing System

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Renbin Liu ◽  
Zhaohui Deng
Keyword(s):  
Steady State ◽  
Size Distribution ◽  
Wireless Local Area Network ◽  
Local Area Network ◽  
Local Area ◽  
System Size ◽  
State System ◽  
System Capacity ◽  
Area Network ◽  
Special Cases

This paper examines a discrete-time modified D-policy Geo/G/1 queue with Bernoulli feedback. Using a decomposition method, the steady-state system size distribution at epochn+is obtained. Moreover, the steady-state system size distributions at epochsn-andnare also derived. Two special cases are given. Finally, a wireless local area network is numerically presented to validate the applicability of steady-state system size distribution and its important application in system capacity design.

scholarly journals Steady-State Analysis of a Flexible Markovian Queue with Server Breakdowns

Entropy ◽  
2019 ◽  
Vol 21 (3) ◽  
pp. 259 ◽  
Author(s):  
Messaoud Bounkhel ◽  
Lotfi Tadj ◽  
Ramdane Hedjar
Keyword(s):  
Steady State ◽  
Probability Generating Function ◽  
Threshold Level ◽  
System Size ◽  
Single Server ◽  
Markovian Queue ◽  
Breakdown Rates ◽  
Bulk Service ◽  
Service Rates ◽  
Number Of Customers

A flexible single-server queueing system is considered in this paper. The server adapts to the system size by using a strategy where the service provided can be either single or bulk depending on some threshold level c. If the number of customers in the system is less than c, then the server provides service to one customer at a time. If the number of customers in the system is greater than or equal to c, then the server provides service to a group of c customers. The service times are exponential and the service rates of single and bulk service are different. While providing service to either a single or a group of customers, the server may break down and goes through a repair phase. The breakdowns follow a Poisson distribution and the breakdown rates during single and bulk service are different. Also, repair times are exponential and repair rates during single and bulk service are different. The probability generating function and linear operator approaches are used to derive the system size steady-state probabilities.

Probabilistic Analysis of Long-Term Climate Drought Using Steady-State Markov Chain Approach

2020 ◽  
Vol 34 (15) ◽  
pp. 4703-4724
Author(s):  
Saeed Azimi ◽  
Erfan Hassannayebi ◽  
Morteza Boroun ◽  
Mohammad Tahmoures
Keyword(s):  
Markov Chain ◽  
Steady State ◽  
Probabilistic Analysis ◽  
Markov Chain Approach

Analysis of Selection Algorithms: A Markov Chain Approach

1996 ◽  
Vol 4 (2) ◽  
pp. 133-167 ◽  
Author(s):  
Uday Kumar Chakraborty ◽  
Kalyanmoy Deb ◽  
Mandira Chakraborty
Keyword(s):  
Genetic Algorithms ◽  
Markov Chain ◽  
Performance Measures ◽  
Finite Population ◽  
Selection Strategy ◽  
Markov Chain Approach ◽  
Population Sizes ◽  
Tournament Selection ◽  
Selection Algorithms ◽  
Compare And Contrast

A Markov chain framework is developed for analyzing a wide variety of selection techniques used in genetic algorithms (GAs) and evolution strategies (ESs). Specifically, we consider linear ranking selection, probabilistic binary tournament selection, deterministic s-ary (s = 3,4, …) tournament selection, fitness-proportionate selection, selection in Whitley's GENITOR, selection in (μ, λ)-ES, selection in (μ + λ)-ES, (μ, λ)-linear ranking selection in GAs, (μ + λ)-linear ranking selection in GAs, and selection in Eshelman's CHC algorithm. The analysis enables us to compare and contrast the various selection algorithms with respect to several performance measures based on the probability of takeover. Our analysis is exact—we do not make any assumptions or approximations. Finite population sizes are considered. Our approach is perfectly general, and following the methods of this paper, it is possible to analyze any selection strategy in evolutionary algorithms.

A DISCRETE-TIME Geo/G/1 RETRIAL QUEUE WITH SERVER BREAKDOWNS

2006 ◽  
Vol 23 (02) ◽  
pp. 247-271 ◽  
Author(s):  
IVAN ATENCIA ◽  
PILAR MORENO
Keyword(s):  
Steady State ◽  
Performance Measures ◽  
Discrete Time ◽  
Continuous Time ◽  
Queueing System ◽  
Retrial Queue ◽  
System Size ◽  
Stochastic Decomposition ◽  
Recursive Procedure ◽  
Server Breakdown

This paper discusses a discrete-time Geo/G/1 retrial queue with the server subject to breakdowns and repairs. The customer just being served before server breakdown completes his remaining service when the server is fixed. The server lifetimes are assumed to be geometrical and the server repair times are arbitrarily distributed. We study the Markov chain underlying the considered queueing system and present its stability condition as well as some performance measures of the system in steady-state. Then, we derive a stochastic decomposition law and as an application we give bounds for the proximity between the steady-state distributions of our system and the corresponding system without retrials. Also, we introduce the concept of generalized service time and develop a recursive procedure to obtain the steady-state distributions of the orbit and system size. Finally, we prove the convergence to the continuous-time counterpart and show some numerical results.

Performance Analysis of a Markovian Queuing System with Reneging and Retention of Reneged Customers

2016 ◽  
pp. 97-105
Author(s):  
Rakesh Kumar
Keyword(s):  
Steady State ◽  
Performance Measures ◽  
Cost Model ◽  
Customer Retention ◽  
System Size ◽  
Retention Mechanism ◽  
Queuing System ◽  
System Capacity ◽  
Service Rate ◽  
Retention Of Reneged Customers

In this chapter a finite capacity single server Markovian queuing system with reneging and retention of reneged customers is considered. It is envisaged that a reneging customer may be convinced to stay for his service if some customer retention mechanism is employed. Thus, there is a probability that a reneging customer may be retained. Steady-state balance equations of the model are derived using Markov chain theory. The steady-state probabilities of system size are obtained explicitly by using iterative method. The performance measures like expected system size, expected rate of reneging, and expected rate of retention are obtained. The effect of probability of retaining a reneging customer on the performance measures is studied. The economic analysis of the model is performed by developing a cost model. The optimum service rate and optimum system capacity are obtained using classical optimization and pattern search techniques. The optimization carried out helps to identify the optimum customer retention strategy from among many.

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