By Attahiru Sule Alfa
Queueing concept purposes may be stumbled on in lots of walks of lifestyles together with; transportation, production, telecommunications, computers and extra. despite the fact that, the main generic purposes of queueing idea are within the telecommunications field.
Queueing idea for Telecommunications: Discrete Time Modelling of a unmarried Node approach makes a speciality of discrete time modeling and illustrates that almost all queueing structures encountered in actual lifestyles will be organize as a Markov chain. this selection is especially exact as the versions are set in one of these method that matrix-analytic equipment are used to investigate them.
Queueing idea for Telecommunications: Discrete Time Modelling of a unmarried Node method is the main correct ebook to be had on queueing versions designed for functions to telecommunications. This e-book provides transparent concise theories at the back of the right way to version and study key unmarried node queues in discrete time utilizing exact instruments that have been offered within the moment bankruptcy. The textual content additionally delves into the categories of unmarried node queues which are very usually encountered in telecommunication platforms modeling, and gives basic tools for examining them. the place acceptable, replacement research tools also are offered.
This e-book is for advanced-level scholars and researchers focusing on engineering, machine technological know-how and arithmetic as a secondary textual content or reference publication. execs who paintings within the similar industries of telecommunications, commercial engineering and communications engineering will locate this e-book worthy in addition.
Read Online or Download Queueing Theory for Telecommunications: Discrete Time Modelling of a Single Node System PDF
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Extra resources for Queueing Theory for Telecommunications: Discrete Time Modelling of a Single Node System
0106 . 0106. 2 Some Key Information Provided by First Passage Deﬁne fi j = ∑∞ n=1 f i j as the probability of the system ever passing from state i to state j. It is clear that (n) • fi j = 1 implies that state j is reachable from state i. • fi j = f ji = 1 implies that states i and j do communicate (n) • fii is the probability that the ﬁrst recurrence time for state i is n. Letting fii = (n) ∑∞ n=1 f ii then • fii = 1 for all recurrent states • fii < 1 for all transient states. Sometimes we are interested mainly in the ﬁrst moment of the passage times.
Also, given that the buffer is now full, what is the probability that the next time that the buffer is full again is at the ﬁfth transition from now? I let the reader ﬁgure this out as an excercise. What we need to calculate is F (4) and select its (2, 4) element. 0144 . 0106 . 0106. 2 Some Key Information Provided by First Passage Deﬁne fi j = ∑∞ n=1 f i j as the probability of the system ever passing from state i to state j. It is clear that (n) • fi j = 1 implies that state j is reachable from state i.
We shall discuss the case of inﬁnite space Markov chains later. e. , the matrix P(n) is the nth order transition matrix of the (n) system. In fact, let pi j be the (i, j)th element of P(n) then we have (2) pi j = (3) pi j = ∑ piv pv j ∑ piv pv j = ∑ piv v∈I v∈I (2) ∑ v∈I (2) piv pv j .. =. 4 Discrete Time Markov Chains 21 Since P(2) = P2 from the ﬁrst of above equation, by a simple induction, we will know P(n) = Pn holds for any non-negative integer n. This is the well known Chapman-Kolmogorov equation.
Queueing Theory for Telecommunications: Discrete Time Modelling of a Single Node System by Attahiru Sule Alfa