SINGLE SERVER RETRIAL QUEUEING SYSTEM WITH VARIABLE SERVICE RATES IN PRIORITY SERVICE BY MATRIX GEOMETRIC METHOD

International Journal of Applied Mathematics and Computation

G. Ayyappan¹  Muthu Ganapathi Subramanian²  Gopal Sekar² 

[1] Pondicherry Engineering College, Pondicherry, India$$;Tagore Arts College, Pondicherry, India$$

关键词: Single Server – Stochastic nature – priority –non-pre-emptive priority service – variable service rates-Matrix Geometric Method – Orbit – classical retrial policy;   

DOI  :  10.0000/ijamc.2011.3.3.150

来源: PSIT Kanpur

【 摘 要 】

Consider a single server retrial queueing system with non-pre-emptive priority service and variable service rates in which two types of customers arrive in a Poisson process with arrival rate λ1 for low priority customers and λ2 for high priority customers.We assume that the regular service times follow an exponential distribution with parameters μ1 and μ2for both types of customers respectively. The retrial is introduced for low priority customers only.The concept of variable service rate (accelerated service) is introduced in this paper and it follows the exponential distribution with parameter µ3. The access from orbit to the service facility follows the classical retrial policy and the high priority customers will be governed by the non-pre-emptive priority service.This model is solved by using Matrix geometric Technique.Numerical  study  have been done for   Analysis of  Mean number of low priority customers in the orbit (Mnco),Mean number of high priority customers in the queue, Truncation level (O_cut),Probability of server free and Probabilities  of server busy with low and high priority customers for various values of λ1 ,  λ2 , μ1 , µ2 , µ3 ,  σ and k  in elaborate manner and also various particular cases of  this model have been discussed.

【 授权许可】

Unknown