2006
DOI: 10.1017/cbo9780511616488
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Performance Analysis of Communications Networks and Systems

Abstract: This rigourous and self-contained book describes mathematical and, in particular, stochastic methods to assess the performance of networked systems. It consists of three parts. The first part is a review on probability theory. Part two covers the classical theory of stochastic processes (Poisson, renewal, Markov and queuing theory), which are considered to be the basic building blocks for performance evaluation studies. Part three focuses on the relatively new field of the physics of networks. This part deals … Show more

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Cited by 206 publications
(170 citation statements)
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“…In the sequel of the paper, we denote the probabilities that a link is in the state ON Fig. 2(a)], we denote a transition probability p that a link present at the moment t will not appear at the moment (t + 1); and probability q that a link will be added at the moment (t + 1), if it was not present at the moment t. According to the Markovian model and the formula for total probability we can calculate the probability for both states ON and OFF [8,34] . In a special case where p + q = 1, there is no time correlation and we have a fixed probability q for a link appearance, which corresponds to Erdős-Rényi temporal network as shown in Fig.…”
Section: B Markov Temporal Modelmentioning
confidence: 99%
“…In the sequel of the paper, we denote the probabilities that a link is in the state ON Fig. 2(a)], we denote a transition probability p that a link present at the moment t will not appear at the moment (t + 1); and probability q that a link will be added at the moment (t + 1), if it was not present at the moment t. According to the Markovian model and the formula for total probability we can calculate the probability for both states ON and OFF [8,34] . In a special case where p + q = 1, there is no time correlation and we have a fixed probability q for a link appearance, which corresponds to Erdős-Rényi temporal network as shown in Fig.…”
Section: B Markov Temporal Modelmentioning
confidence: 99%
“…The results for G 0.2 (N) are plotted in Figures 10-13. Figures 10 and 11 indicate that the difference in weight decreases when N increases, because E[w(P )] ≈ ln N Np [19]. The probability density function for w(P 2 ) − w(P 1 ) in Figure 10 seems to follow an exponential distribution, unlike the probability density function for w(P l ) − w(P 1 ) in Figure 11.…”
Section: Bounds On Path Stabilitymentioning
confidence: 95%
“…The broker receives the current status of data centers' physical resources and their energy information from ECE-CIS, and based on this information, assigns the VM to a physical server in a data center site. Based on [25], in today's Internet and core networks design, average number of hops a packet passes from source to destination is between 12-14 hops. Therefore, we can have data center site selection without considering network distance; especially for sites that are located in a region, such as different states in USA, as we considered in this paper.…”
Section: Ece Cloud Informationmentioning
confidence: 99%