Multi-server retrial queue with second optional service: algorithmic computation and optimisation

Ke, Jau‐Chuan; Wu, Chia-Huang; Pearn, W. L.

doi:10.1080/00207721003650209

Cited by 10 publications

(3 citation statements)

References 31 publications

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“…A single-server retrial queue with calls of finite number as sources of is investigated by Falin and Artalejo (1998). Ke et al (2011) presents a mathematically way for the evaluation a call centre miniature, server with single vacation. Phung-Duc and Kawanishi (2014) proposed a M/M/c retrial queue miniature with balking and after-call work for call centres.…”

Section: Introductionmentioning

confidence: 99%

Genetic algorithm in retrial queueing system with server breakdown and caller intolerance with voluntary service

Jain

2021

Int J Syst Assur Eng Manag

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The paper investigates the M/M/s retrial queueing system with servers prone to breakdown and with voluntary service. During a phone call, if the caller finds a free call line, then it connects immediately to the call agent, considered as server. Those who finds the call busy either join the orbit for retrial or disconnect the call. After receiving the essential service either caller leaves the system or requests for voluntary service. The miniature used in the queueing system employs a quasi-birth-and-death process. The stationary probabilities are derived using matrix-analytic approach and then performance measures are calculated using these stationary probabilities. The impact of system parameters on performance measures is illustrated using graphs and tables. Total system cost is calculated as a function of orbit capacity, repair rate of breakdown and two different service rates. The optimization methodology is demonstrated using various cases. Further the Genetic algorithm is used to find the optimum value of both essential and optional service rates, rate of breakdown and orbit capacity to minimize the overall cost. The study of consistency of retrial queue with server prone to breakdowns and repairs is of great significance because of inadequate capability of repairs and strong impact of the breakdowns on the performance measures.

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Section: Introductionmentioning

confidence: 99%

Genetic algorithm in retrial queueing system with server breakdown and caller intolerance with voluntary service

Jain

2021

Int J Syst Assur Eng Manag

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“…But the analysis of retrial queue in continuous time case has been considered by many authors. The interested reader may see Almasi, Roszik, and Sztrik (2005), Artalejo and Lopez-Herrero (2007), Krishnakumar and Raja (2006), Krishnakumar, Rukmani, and Thangaraj (2009), Ke, Wu, and Pearn (2011) and Amirthakodi and Sivakumar (2014).…”

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confidence: 98%

An inventory system with two types of customers and retrial demands

Karthick

Arivarignan

2015

International Journal of Systems Science: Operations & Logi

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We consider a continuous review (s, S) inventory system in which the arriving customers belong to any one of the two types (type-1 or type-2). When the inventory level is above s, the customers are not distinguished as to their type and their demanded items are delivered immediately to them. Once the inventory level drops to s(≥ 0), an order for Q items is placed and thereafter the demands of type-2 customers alone are satisfied. The type-1 customers are sent to a place called orbit which is of infinite size. These orbiting demands retry for their demand after a random time which is assumed to have exponential distribution. The arrivals of customers are assumed to follow a Markovian arrival process and the lead time is assumed to have phase-type distribution. The joint probability distribution of the number of customers in the orbit and the inventory level is obtained in the steady-state case. Various system performance measures in the steady state are derived and total expected cost rate is calculated.

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“…In some queueing situations all arriving customers require the essential service, whereas a few of them may further demand the subsidiary service provided by the same server immediately after completion of the regular service. Several researchers have studied the concept of additional optional service with queues [11,19,20]. Jeganathan [9] investigated a continuous review perishable (s, S) inventory system with N optional services, in which some of the arriving customers asked for second optional service as soon as the completion of first essential service and the second service is multi-optional.…”

Section: Introductionmentioning

confidence: 99%

A retrial queueing-inventory system with J-additional options for service and finite source

Yadavalli

Jeganathan

Venkatesan

et al. 2017

ORiON

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A continuous review (s, S) inventory system at a service facility with finite homogeneous sources of demands and retrial is analysed. The lifetime of each item is assumed to be exponential. Before items are delivered to the customers, some basic service on the item must be performed. It is known as a regular or main service. The service may get interrupted according to a Poisson process and it restarts after an exponentially distributed time. If the server is idle at the time of arrival of a customer and the inventory level is positive, then the service begins immediately. After the completion of regular service, a customer may either abandon the system forever or demand for a second service from the same server, which is multi-optional. If any arriving customer finds that the server is busy or inventory level is zero, he/she either enters into the orbit with probability p or balks (does not enter) with probability 1 − p. The stationary distribution of the number of customers in the system, server status and the inventory level is obtained by the matrix method. The Laplace-Stieltjes transform of the waiting time of the tagged customer is derived. Various system performance measures are derived and the total expected cost rate is computed under a suitable cost structure. A numerical illustration is given.

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Multi-server retrial queue with second optional service: algorithmic computation and optimisation

Cited by 10 publications

References 31 publications

Genetic algorithm in retrial queueing system with server breakdown and caller intolerance with voluntary service

Genetic algorithm in retrial queueing system with server breakdown and caller intolerance with voluntary service

An inventory system with two types of customers and retrial demands

A retrial queueing-inventory system with J-additional options for service and finite source

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