By Attahiru Alfa
This book introduces the theoretical basics for modeling queues in discrete-time, and the fundamental methods for constructing queuing versions in discrete-time. there's a concentrate on functions in glossy telecommunication systems.
It presents how so much queueing versions in discrete-time will be arrange as discrete-time Markov chains. options reminiscent of matrix-analytic equipment (MAM) that may used to research the ensuing Markov chains are integrated. This e-book covers unmarried node structures, tandem process and queueing networks. It indicates how queues with time-varying parameters should be analyzed, and illustrates numerical concerns linked to computations for the discrete-time queueing platforms. optimum keep an eye on of queues is additionally covered.
Applied Discrete-Time Queues ambitions researchers, advanced-level scholars and analysts within the box of telecommunication networks. it's appropriate as a reference publication and will even be used as a secondary textual content ebook in laptop engineering and machine science. Examples and routines are included.
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Additional resources for Applied Discrete-Time Queues
Dm1 dm2 · · · dmn 1. e. each element ai,j of this matrix has the property that 0 ≤ ai,j < ∞, 2. an n row vector c = [c1 , c2 , · · · , cn ], and ⎡ ⎤ b1 ⎢ b2 ⎥ ⎢ ⎥ 3. an n column vector b = ⎢ . ⎥. ⎣ .. ⎦ bn 4. A column vector 1 = [1 1 · · · 1]T , where AT is the transpose of a matrix A 5. ej (n) which is an n column vector of zeros in all locations except at location j where there is a 1. 6. An identity matrix I. e. of dimension n. We have the following properties of matrices that will be used in this book 1.
Let J1 := (Xn (e) ≤ Ke , Xn (r) ≤ K − Ke ), J2 := (Xn (e) ≤ Ke , Xn (r) ≥ K − Ke ), J3 := (Xn (e) ≥ Ke , Xn (r) ≤ K − Ke ), J4 := (Xn (e) ≥ Ke , Xn (r) ≥ K − Ke ), where A := C implies that A is equivalent to C. Then we have ⎧ ⎪ ⎪ ⎨ (Ae , Ar ), J1 , J2 , (Ae , ((Xn (r) − K + Ke )+ + Ar )), (Xn+1 (e), Xn+1 (r)) = ⎪ J3 , ((Xn (e) − Ke )+ + Ae , Ar ), ⎪ ⎩ ((Xn (e) − Ke )+ + Ae , (Xn (r) − K + Ke )+ + Ar )), J4 . Again from this we can study how the queues of regular and emergency patients grow with time.
Implying that everything that occurs after time tn and throughout the interval up to time tn+1 , is observable at time tn+1 ; for example all arrivals to a system that occur between the interval (tn , tn+1 ] are observed, and assume to take place, at time epoch tn+1 . Another way to look at it is that nothing occurs between the interval (tn , tn+1 ] that is not observable at time epoch tn+1 . By this reasoning we assume the picture of the system is frozen at these time points t1 , t2 , · · · , tn , · · · , and also assume that it takes no time to “freeze" the picture.
Applied Discrete-Time Queues by Attahiru Alfa