By Masakiyo Miyazawa (auth.), Wuyi Yue, Yataka Takahashi, Hideaki Takagi (eds.)
Advances in Queueing conception and community Applications offers a number of necessary mathematical analyses in queueing conception and mathematical versions of key applied sciences in stressed and instant verbal exchange networks equivalent to channel entry controls, web functions, topology building, strength saving schemes, and transmission scheduling. In 16 top quality chapters, this paintings offers novel principles, new analytical versions, and simulation and experimental effects through specialists within the box of queueing thought and community applications.
The textual content serves as a cutting-edge reference for a variety of researchers and engineers engaged within the fields of queueing conception and community functions, and will additionally function supplemental fabric for complex classes in operations learn, queueing idea, functionality research, site visitors idea, in addition to theoretical layout and administration of conversation networks.
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Ma et al. vacation policy. For example, M/G/1 queues with multiple types of feedback and gated vacations were studied, and some important results were derived in [3]. A number of discrete time queue models were studied in [4] and [5]. Also, Wu and Takagi studied the queue model with working vacations in [6], and extended the general vacation polity. The new queue model enriched the theory of the queue with vacations, and involved many queue models as special cases. A discrete time GI/Geo/1 queue model with multiple vacations was studied in [7].
3 to this model. For this, we need to compute θ (−c) , θ (+c) (c) and η2 . 2, they are obtained if we can solve the following three sets of equations. 27) (1−) (θ1 ) + ϕ1 (1+) (θ1 ) + ϕ1 = 1, ϕ0 = 1, ϕ0 (+) (+) (+) X1 +η2 X2 = 1, E eη1 (−) (2) = 1, (+) ϕ−1 (η2 )e−η1 + ϕ0 (η2 ) + ϕ1 (η2 )eη1 (2) (2) = 1. 26). Then, we have λ1 z + μ2 zξ −1 + μ1 z−1 + (λ2 + δ )z−1 ξ = 1, λ1 z + μ2 + μ1 z−1 + (λ2 + δ )z−1 ξ = 1. 30) Solving these equations for z = 1, we have z = ξ = ρ1−1 . 29) yields ξ = ρ1−1 , λ μ+2 δ ρ1−1 .
7) Because the two kinds of customers are mutually independent, we have that Lv (z) = (1 − ρ )(1 − z)S(1 − p(1 − z)) Qb (z) − Qb (0) × . 8) 3 A Pure Decrement Service Geom/G/1 Queue with MAVs 55 (1 − ρ )(1 − z)S(1 − p(1 − z)) S(1 − p(1 − z)) − z 1 −V (1 − p(1 − z)) + H(V ( p))V ¯ (1 − p(1 − z)) − H(V ( p))z ¯ × (H(V ( p)) ¯ + pE[V ](1 − H(V ( p))))(1 ¯ − z) (1 − pE[V ])(1 − z) × V (1 − p(1 − z)) − z = L(z)Ld (z)Lr (z). F. of the system queue length in the FCFS service strategy. 1, we have that Ld (z) = H(V ( p)) ¯ H(V ( p)) ¯ + pE[V ](1 − H(V ( p))) ¯ 1 −V (1 − p(1 − z)) pE[V ](1 − H(V ( p))) ¯ × .