scholarly journals A monotonicity result for a G/GI/c queue with balking or reneging

2006 ◽  
Vol 43 (04) ◽  
pp. 1201-1205
Author(s):  
Serhan Ziya ◽  
Hayriye Ayhan ◽  
Robert D. Foley ◽  
Erol Peköz
Keyword(s):  
Loss System ◽  
Fixed Probability ◽  
Monotonicity Result

In a G/GI/c loss system with balking, reneging, or limited waiting space, deleting some of the arriving customers can either increase or decrease the fraction of the remaining arrivals who get served, depending on how customers are deleted. We present a model in which the random deletion of arrivals independently and with some fixed probability can never decrease the fraction of the remaining arrivals who get served.

scholarly journals A monotonicity result for a G/GI/c queue with balking or reneging

2006 ◽  
Vol 43 (4) ◽  
pp. 1201-1205 ◽  
Author(s):  
Serhan Ziya ◽  
Hayriye Ayhan ◽  
Robert D. Foley ◽  
Erol Peköz
Keyword(s):  
Loss System ◽  
Fixed Probability ◽  
Monotonicity Result

In a G/GI/c loss system with balking, reneging, or limited waiting space, deleting some of the arriving customers can either increase or decrease the fraction of the remaining arrivals who get served, depending on how customers are deleted. We present a model in which the random deletion of arrivals independently and with some fixed probability can never decrease the fraction of the remaining arrivals who get served.

A monotonicity result for a single-server loss system

1995 ◽  
Vol 32 (04) ◽  
pp. 1112-1117
Author(s):  
Xiuli Chao ◽  
Liyi Dai
Keyword(s):  
Markov Process ◽  
Infinitesimal Generator ◽  
Blocking Probability ◽  
Matrix Analysis ◽  
Service Process ◽  
Single Server ◽  
Loss System ◽  
Special Cases ◽  
Monotonicity Result ◽  
Loss Systems

We consider a family of M(t)/M(t)/1/1 loss systems with arrival and service intensities (λt (c), μt (c)) = (λct , μct ), where (λt , μt ) are governed by an irreducible Markov process with infinitesimal generator Q = (qij )m × m such that (λt , μt ) = (λi , μi ) when the Markov process is in state i. Based on matrix analysis we show that the blocking probability is decreasing in c in the interval [0, c ∗], where c ∗ = 1/maxi Σ j ≠i qij /(λi + μi ). Two special cases are studied for which the result can be extended to all c. These results support Ross's conjecture that a more regular arrival (and service) process leads to a smaller blocking probability.

A monotonicity result for a single-server loss system

1995 ◽  
Vol 32 (4) ◽  
pp. 1112-1117 ◽  
Author(s):  
Xiuli Chao ◽  
Liyi Dai
Keyword(s):  
Markov Process ◽  
Infinitesimal Generator ◽  
Blocking Probability ◽  
Matrix Analysis ◽  
Service Process ◽  
Single Server ◽  
Loss System ◽  
Special Cases ◽  
Monotonicity Result ◽  
Loss Systems

We consider a family of M(t)/M(t)/1/1 loss systems with arrival and service intensities (λt (c), μt (c)) = (λct, μct), where (λt, μt) are governed by an irreducible Markov process with infinitesimal generator Q = (qij)m × m such that (λt, μt) = (λi, μi) when the Markov process is in state i. Based on matrix analysis we show that the blocking probability is decreasing in c in the interval [0, c∗], where c∗ = 1/maxi Σj≠iqij/(λi + μi). Two special cases are studied for which the result can be extended to all c. These results support Ross's conjecture that a more regular arrival (and service) process leads to a smaller blocking probability.

Finiteness of moments of partial busy periods for M/G/C queues

1986 ◽  
Vol 23 (1) ◽  
pp. 261-264 ◽  
Author(s):  
Saeed Ghahramani
Keyword(s):  
Busy Period ◽  
Loss System

Conditions for finiteness of moments of the following quantities have been found: the duration of a busy period of an Μ /G/∞ system; the duration of a partial busy period of an M/G/C loss system, and the duration of a partial busy period of an M/G/C queue.

Optimal Input for the Loss System G/M/2

1976 ◽  
Vol 7 (1) ◽  
pp. 129-137 ◽  
Author(s):  
Klaus Fleischmann
Keyword(s):  
Loss System ◽  
Optimal Input
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