GSPN analysis of retrial systems with servers breakdowns and repairs

Gharbi, Nawel; Ioualalen, Malika

doi:10.1016/j.amc.2005.06.005

Cited by 27 publications

(15 citation statements)

References 11 publications

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“…It integrates the essential features of concurrency, synchronisation and a sequenced presentation of complex systems. The GSPNs have been successfully used (Jayaparvathy et al, 2007;Ciardo et al, 1991;Gharbi and Ioualalen, 2006;Gharbi et al, 2009) to analyse complex CTMC in a concise way, thereby facilitating a graphical visualisation of a multi-tasking scenario and a dynamic behaviour of a system.…”

Section: The Gspn Modelmentioning

confidence: 99%

On the study of simultaneous service by random number of servers with retrial and preemptive priority

Vinayak

Selvamuthu

Arunachalam

2014

IJOR

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In this paper, we propose to study the performance of a multi-server queuing system in which a customer requires simultaneous service from a random number of servers with the queuing disciplines retrial and preemptive priority. The infinitesimal generator matrix is presented for the proposed model and steady state measures are discussed. In particular, analytical expressions are obtained for the case where a customer (single type) requires simultaneous service from a random number of servers. Also, the generalised stochastic Petri net (GSPN) is developed for the proposed model and the particular cases. The performance of the models is analysed and compared, in terms of average system size and throughput. It is found that queuing systems in which a customer requires simultaneous service from a random number of servers performs better when the queuing discipline of retrial is appended into the system.

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Section: The Gspn Modelmentioning

confidence: 99%

On the study of simultaneous service by random number of servers with retrial and preemptive priority

Vinayak

Selvamuthu

Arunachalam

2014

IJOR

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“…Li and Yang (1995) treat the FSRQ with vacation. During the last decade, an important number of papers on this topic have been published Almasi et al (2005) (Homogeneous FSRQ), Gharbi and Ioualalen (2006), use the Markovian GSPN to analyze retrial systems and Zhang and Wang (2013), Wang et al (2011), etc. The orbital search behavior introduced in with the purpose to reduce the server's idle time. After termination of service, with probability p the server required to search for customer from the orbit.…”

Section: Introductionmentioning

confidence: 99%

MRSPN analysis of Semi-Markovian finite source retrial queues

2015

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In this paper, the analysis of Semi-Markovian single server retrial queues by means of Markov Regenerative Stochastic Petri Nets (MRSPN) is considered. We propose MRSPN models for the two retrial queues M/G/1/N/N and M/G/1/N/N with orbital search. By inspecting the reduced reachability graph of both MRSPN models, the qualitative analysis is obtained. The quantitative analysis is carried out after constructing their one step transition probability matrix and computing the steady state probability distribution of each tangible marking. As an example, the queue M/H ypo 2 /1/2/2 is treated in order to illustrate the functionality of the MRSPN approach. The exact performance measures (mean number of customers in the system, mean response time, mean waiting time,…) are computed for different parameters of the two systems by an algorithm elaborated in Matlab environment.

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“…Owing to the utility and interesting mathematical properties of retrial queueing models, a vast literature on the subject has emerged over the past several decades. For a general survey of retrial queues and a summary of many results, the reader is directed to the works of [6,8,7,5,12,15] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Performance evaluation of two Markovian retrial queueing model with balking and feedback

Bouchentouf

Belarbi

2013

Acta Universitatis Sapientiae, Mathematica

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In this paper, we consider the performance evaluation of two retrial queueing system. Customers arrive to the system, if upon arrival, the queue is full, the new arriving customers either move into one of the orbits, from which they make a new attempts to reach the primary queue, until they find the server idle or balk and leave the system, these later, and after getting a service may comeback to the system requiring another service. So, we derive for this system, the joint distribution of the server state and retrial queue lengths. Then, we give some numerical results that clarify the relationship between the retrials, arrivals, balking rates, and the retrial queue length.

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GSPN analysis of retrial systems with servers breakdowns and repairs

Cited by 27 publications

References 11 publications

On the study of simultaneous service by random number of servers with retrial and preemptive priority

On the study of simultaneous service by random number of servers with retrial and preemptive priority

MRSPN analysis of Semi-Markovian finite source retrial queues

Performance evaluation of two Markovian retrial queueing model with balking and feedback

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