By Masakiyo Miyazawa (auth.), Wuyi Yue, Yataka Takahashi, Hideaki Takagi (eds.)

ISBN-10: 0387097023

ISBN-13: 9780387097022

ISBN-10: 0387097031

ISBN-13: 9780387097039

*Advances in Queueing concept and community Applications* offers a number of priceless mathematical analyses in queueing idea and mathematical versions of key applied sciences in stressed out and instant communique networks reminiscent of channel entry controls, net purposes, topology building, strength saving schemes, and transmission scheduling. In 16 top quality chapters, this paintings offers novel rules, new analytical types, and simulation and experimental effects through specialists within the box of queueing idea and community applications.

The textual content serves as a state of the art reference for a variety of researchers and engineers engaged within the fields of queueing idea and community functions, and will additionally function supplemental fabric for complicated classes in operations examine, queueing conception, functionality research, site visitors concept, in addition to theoretical layout and administration of conversation networks.

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5) m=1 where M(t) is the number of parent multicasts in [0,t). , [8], [9]). This renewal reward representation is used in the following section to derive the average download rate. 3 Mean Download Rate and Optimal Strategy We now find the optimal merging limit time x0 that minimizes the average download rate from the streaming server. Let b(x) be the average download rate given the merging limit time x, or b(x) = lim t→∞ S(t) . 6) 40 H. Toyoizumi b x 100 80 60 40 20 20 40 60 80 100 x Fig. 4 The download rate b(x) and the merging limit time x: the request arrival rate λ = 1, and the content size s = 100.

This concludes that f is maximized at (z1 (ξ ∗ ), z2 (ξ ∗ ), ξ ∗ ) such that z1 (ξ ∗ ) = z1 (ξ ∗ ). Since ξ ∗ must be the maximum value of ξ satisfying g1 (z1 , z2 , ξ ) = 0, η2 = θ2− max . This completes the proof. , see Sect. 7 of [11]). However, the present solution is more informative since the feasible region D is identified to be a connected curve. (c) References 1. M. Miyazawa, “Tail decay rates in a doubly QBD process,” Submitted for publication. 2. M. Miyazawa, “Doubly QBD process and a solution to the tail decay rate problem,” in Proc.

Foley and D. R. McDonald, “Bridges and networks: Exact asymptotics,” The Annals of Applied Probability, vol. 15, pp. 542-586, 2005. 11. M. S. Bazaraa, H. D. Sherali, and C. M. Shetty, Nonlinear Programming: Theory and Algorithms. New York: Wiley, 1993. Chapter 2 Analytical Model of On-Demand Streaming Services Based on Renewal Reward Theory Hiroshi Toyoizumi Abstract We propose an analytical model based on renewal reward theory to investigate the dynamics of an on-demand streaming service. At the same time, we also propose a simple method combining a method of multicasts and method of unicasts that can reduce the download rate from the streaming server without causing delay.

### Advances in Queueing Theory and Network Applications by Masakiyo Miyazawa (auth.), Wuyi Yue, Yataka Takahashi, Hideaki Takagi (eds.)

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