By Masakiyo Miyazawa (auth.), Wuyi Yue, Yataka Takahashi, Hideaki Takagi (eds.)
Advances in Queueing thought and community Applications provides a number of beneficial mathematical analyses in queueing conception and mathematical types of key applied sciences in stressed and instant conversation networks corresponding to channel entry controls, web purposes, topology development, strength saving schemes, and transmission scheduling. In 16 fine quality chapters, this paintings offers novel rules, new analytical types, and simulation and experimental effects via specialists within the box of queueing conception and community applications.
The textual content serves as a state of the art reference for quite a lot of researchers and engineers engaged within the fields of queueing idea and community functions, and will additionally function supplemental fabric for complex classes in operations study, queueing conception, functionality research, site visitors idea, in addition to theoretical layout and administration of conversation networks.
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Extra info for Advances in Queueing Theory and Network Applications
We give some conclusions and remarks in Sect. 5. 2 Streaming Services and Renewal Model Assume the server has only one content of the length s, and its download rate of each stream is 1. The arrival of requests is assumed to be a Poisson process with the rate λ . Although this assumption is a mathematical convention, there is research that we can observe a Poisson arrival at the multimedia server in some cases . Suppose that a request arrives at the server at time 0, and the server starts a multicast for this request.
Those who requested later than the start of multicast miss the initial part of the stream. Thus, we propose a simple method using both the unicast and multicast reducing download rate without causing delay. The objective of our method is to reduce the bandwidth required for the streaming server. Assume there is only one content on the streaming server, for simplicity. We may extend our model to the heterogeneous contents environment, by modeling virtual streaming servers for each content, and treat them separately.
F. Wd (z) of the stationary waiting time Wd as follows: Wd (z) = H(V ( p)) ¯ H(V ( p)) ¯ + pE[V ](1 − H(V ( p))) ¯ 1 −V (z) pE[V ](1 − H(V ( p))) ¯ × . 16) Therefore, the additional delay Wd is equal to zero with the following probability, H(V ( p)) ¯ H(V ( p)) ¯ + pE[V ](1 − H(V ( p))) ¯ and is equal to a vacation time with the following probability, 3 A Pure Decrement Service Geom/G/1 Queue with MAVs 57 pE[V ](1 − H(V ( p))) ¯ . 15) and using L’Hospital’s rule, we can get the mean waiting time E[Wv ] of a customer during a steady state for a Geom/G/1 (PD, MAVs) queue system as follows: E[Wv ] = pE[V (V − 1)](1 − H(V ( p))) ¯ pE[V (V − 1)] pE[S(S − 1)] + + .