Single server retrial queue with group admission of customers. (September 2015)
- Record Type:
- Journal Article
- Title:
- Single server retrial queue with group admission of customers. (September 2015)
- Main Title:
- Single server retrial queue with group admission of customers
- Authors:
- Dudin, A.N.
Manzo, R.
Piscopo, R. - Abstract:
- Abstract: We consider a retrial queueing system with a single server and novel customer׳s admission discipline. The input flow is described by a Markov Arrival Process. If an arriving customer meets the server providing the service, it goes to the orbit and repeats attempts to get service in random time intervals whose duration has exponential distribution with parameter dependent on the customers number in orbit. Server operates as follows. After a service completion epoch, customers admission interval starts. Duration of this interval has phase type distribution. During this interval, primary customers and customers from the orbit are accepted to the pool of customers which will get service after the admission interval. Capacity of this pool is limited and after the moment when the pool becomes full before completion of admission interval all arriving customers move to the orbit. After completion of an admission interval, all customers in the pool are served simultaneously by the server during the time having phase type distribution depending on the customers number in the pool. Using results known for Asymptotically Quasi-Toeplitz Markov Chains, we derive stability condition of the system, compute the stationary distribution of the system states, derive formulas for the main performance measures and numerically show advantages of the considered customer׳s admission discipline (higher throughput, smaller average number of customers in the system, higher probability to getAbstract: We consider a retrial queueing system with a single server and novel customer׳s admission discipline. The input flow is described by a Markov Arrival Process. If an arriving customer meets the server providing the service, it goes to the orbit and repeats attempts to get service in random time intervals whose duration has exponential distribution with parameter dependent on the customers number in orbit. Server operates as follows. After a service completion epoch, customers admission interval starts. Duration of this interval has phase type distribution. During this interval, primary customers and customers from the orbit are accepted to the pool of customers which will get service after the admission interval. Capacity of this pool is limited and after the moment when the pool becomes full before completion of admission interval all arriving customers move to the orbit. After completion of an admission interval, all customers in the pool are served simultaneously by the server during the time having phase type distribution depending on the customers number in the pool. Using results known for Asymptotically Quasi-Toeplitz Markov Chains, we derive stability condition of the system, compute the stationary distribution of the system states, derive formulas for the main performance measures and numerically show advantages of the considered customer׳s admission discipline (higher throughput, smaller average number of customers in the system, higher probability to get a service without visiting the orbit) in case of proper choice of the capacity of the pool and the admission period duration. … (more)
- Is Part Of:
- Computers & operations research. Volume 61(2015)
- Journal:
- Computers & operations research
- Issue:
- Volume 61(2015)
- Issue Display:
- Volume 61, Issue 2015 (2015)
- Year:
- 2015
- Volume:
- 61
- Issue:
- 2015
- Issue Sort Value:
- 2015-0061-2015-0000
- Page Start:
- 89
- Page End:
- 99
- Publication Date:
- 2015-09
- Subjects:
- Retrial queueing system -- Group admission -- Stationary distribution -- Optimization
Operations research -- Periodicals
Electronic digital computers -- Periodicals
004.05 - Journal URLs:
- http://www.sciencedirect.com/science/journal/03050548 ↗
http://www.elsevier.com/journals ↗ - DOI:
- 10.1016/j.cor.2015.03.008 ↗
- Languages:
- English
- ISSNs:
- 0305-0548
- Deposit Type:
- Legaldeposit
- View Content:
- Available online (eLD content is only available in our Reading Rooms) ↗
- Physical Locations:
- British Library DSC - 3394.770000
British Library DSC - BLDSS-3PM
British Library HMNTS - ELD Digital store - Ingest File:
- 2493.xml