scholarly journals Loss Probability of LRD and SRD Traffic in Generalized Processor Sharing Systems

2007 ◽  
Author(s):  
Xiaolong Jin ◽  
Geyong Min
Keyword(s):  
Loss Probability ◽  
Processor Sharing ◽  
Generalized Processor Sharing

AnRG-Factorization Approach for a BMAP/M/1 Generalized Processor-Sharing Queue

2005 ◽  
Vol 21 (2-3) ◽  
pp. 507-530 ◽  
Author(s):  
Quan-Lin Li ◽  
Zhaotong Lian ◽  
Liming Liu
Keyword(s):  
Processor Sharing ◽  
Factorization Approach ◽  
Generalized Processor Sharing

Analysis of generalized processor-sharing systems with two classes of customers and exponential services

2004 ◽  
Vol 41 (3) ◽  
pp. 832-858 ◽  
Author(s):  
Fabrice Guillemin ◽  
Didier Pinchon
Keyword(s):  
Hilbert Problem ◽  
Probability Distributions ◽  
Probability Generating Function ◽  
Joint Probability ◽  
Processor Sharing ◽  
Generalized Processor Sharing ◽  
Quarter Plane ◽  
Explicit Formulae ◽  
Gps System ◽  
Number Of Customers

We derive in this paper closed formulae for the joint probability generating function of the number of customers in the two FIFO queues of a generalized processor-sharing (GPS) system with two classes of customers arriving according to Poisson processes and requiring exponential service times. In contrast to previous studies published on the GPS system, we show that it is possible to establish explicit expressions for the generating functions of the number of customers in each queue without calling for the formulation of a Riemann–Hilbert problem. We specifically prove that the problem of determining the unknown functions due to the reflecting conditions on the boundaries of the positive quarter plane can be reduced to a Poisson equation. The explicit formulae are then used to derive some characteristics of the GPS system (in particular the tails of the probability distributions of the numbers of customers in each queue).

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