Applied Discrete-Time Queues by Attahiru Alfa

By Attahiru Alfa

This book introduces the theoretical basics for modeling queues in discrete-time, and the fundamental strategies for constructing queuing versions in discrete-time. there's a specialize in purposes in glossy telecommunication systems.

It presents how so much queueing types in discrete-time could be organize as discrete-time Markov chains. suggestions corresponding to matrix-analytic equipment (MAM) which may used to investigate the ensuing Markov chains are incorporated. This e-book covers unmarried node platforms, tandem process and queueing networks. It exhibits how queues with time-varying parameters could be analyzed, and illustrates numerical matters linked to computations for the discrete-time queueing platforms. optimum regulate of queues can also be covered.

Applied Discrete-Time Queues ambitions researchers, advanced-level scholars and analysts within the box of telecommunication networks. it truly is compatible as a reference booklet and will even be used as a secondary textual content e-book in machine engineering and machine science.  Examples and routines are included.

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7 illustrates this idea. In addition, we only know what we observe at the time points and they constitute the only knowledge we have about the system. Whatever activities occur between our last observation of the system at time tn , and our next observation at time tn+1 , are assumed to occur at time tn+1 . g. a data packet requires at least one time slot for processing, and hence it will be in the system for at least that duration before departing. e. arrivals occur just before the end of an epoch, services terminate at the end of an epoch and the arriving customer is blocked from entering an empty service facility until the servicing interval terminates.

3 A tandem queueing systems 9 system is very common at the in-buffer queue of a switch in communication networks, the check-out counter in a grocery store, at a bank where tellers attend to customers, a commercial parking lot where the parking bays are the servers and the service times are durations of parking, etc. g. roundrobin, table polling, etc. This is called a polling system. This type of queueing system is very common in telecommunication systems in the medium access control (MAC) where packets from different sources arrive at a router and need to be processed and given access to the medium.

Let us assume that each patient takes exactly one unit of time to be vaccinated. Let Xn be the number of people currently receiving or waiting for vaccination at time n and A be the number of arriving patients at any time interval, then we have Xn+1 = A, Xn ≤ K . Xn − K + A, Xn > K This is a very simple example. We can see that the queue build up can be captured by studying Xn , n = 1, 2, 3, · · · . Consider the case where we have K beds in an operating theater, of which Ke < K are reserved for emergency cases.

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