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Waiter the multiple vacation N - strategy M / G ( a , b ) / 1 queuing system research

Author: XiongGuiWu
Tutor: GaoShiZe
School: Chongqing Normal University
Course: System theory
Keywords: Vacation queue M / G (a, b) / 1 Captain Fallow period Busy period
CLC: F224
Type: Master's thesis
Year: 2005
Downloads: 116
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Abstract


Vacation queuing system is a very important queuing model queuing theory . This paper first introduces home and abroad on the topic , as well as dynamic repairable queuing system , and then the waiter has multiple vacation N-policy M/G/1 queuing system based on the introduction of two threshold parameters a , b, defined M / G (a, b) / 1 queuing system with the waiter multiple vacation N- strategy . Using the supplementary variable method, the direct probability method and updated theory methods , the waiter the multiple vacation N- policy M / G (a, b) / 1 queuing system the following results : 1 , under equilibrium conditions at any time t the captain 's mother function expression : P ( z) = [ [R * ( λ - λx (z ) ) -1] (sum from i = a to b -1 ( the Z b < / sup >-z i ) p i ) (z b -1) (R * (λ-λX ( z)) -1) sum from i = 0 to a-1 p i z i (z b -1) (V * (λ-λX (z)) -1) S * (λ-λX (z)) (sum from i = 0 to a-1 p i < / sub> z i sum from i = 0 to N-1 q i z i )] [(-λ λX (z)) ( the z b - S * < / sup> ( λ - λX ( z )) ) ] 2, the system average captain : L = [f 1 ( X, S) sum from i = a to b-1 (b (b-1)-i (i-1) p 1 f 2 (X, S) sum from i = a to b-1 (b-1) p i f 3 (X, S, R) sum from i = 0 to a-1 p < sub> i f 4 (X, S, R, V) (sum from i = 0 to a-1 p i sum from i = 0 to N-1 q i ) f 5 (X, S, R) sum from i = 0 to a-1 ip i f 6 (X, S, R, V) (sum from i = 0 to a-1 ip i sum from i = 0 to N-1 iq i ) ] [ 2 ( λE ( X ) ( B -SL ) 2 ] 3 , the idle period , the average length : E (I) = E (V) / (P (U = 0) ) E (R) 4, the average length of the busy period : E ( B ) = E ( S ) / P (J = 0) = E ( S ) / SUM from i = 0 to a-1 P i < / sub> Finally , to establish the cost of the system model , and a specific instance of a numerical calculation .

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