Download An Introduction to Queueing Systems by Sanjay K. Bose (auth.) PDF

By Sanjay K. Bose (auth.)

ISBN-10: 1461348803

ISBN-13: 9781461348801

ISBN-10: 146150001X

ISBN-13: 9781461500018

Queueing is a side of recent lifestyles that we come upon at each step in our day-by-day actions. no matter if it occurs on the checkout counter within the grocery store or in gaining access to the web, the fundamental phenomenon of queueing arises each time a shared facility should be accessed for provider by way of a ]arge variety of jobs or clients. The examine of queueing is critical because it gravides either a theoretical history to the type of provider that we may possibly count on from this sort of facility and how during which the ability itself will be designed to supply a few certain grade of provider to its shoppers. Our examine of queueing was once primarily encouraged by way of its use within the examine of communique structures and laptop networks. some of the desktops, routers and switches in any such community will be modelled as person queues. the full procedure could itself be modelled as a queueing community supplying the mandatory carrier to the messages, packets or cells that have to be carried. software of queueing thought offers the theoretical framework for the layout and examine of such networks. the aim of this booklet is to help a path on queueing platforms on the senior undergraduate or graduate Ievels. the sort of path could then give you the theoretical historical past on which a next direction at the functionality modeHing and research of machine networks will be based.

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2. Basic Queueing Theory 39 Burke's Theorem: The following three statements hold for the departure process from a M/M/m/oo queue - [A] [B] [C] The departure process from a M/M/m/oo queue is Poisson in nature. For a MIM/m/oo queue, at each time t, the number of customers in the system is independent of the sequence of departure tim es prior to t. For a M/M/m/oo FCFS queue, given a customer departure at time t, the arrival time of this customer is independent of the departure process prior tot. Statement [A] from Burke's Theorem will actually be very useful to analyse networks of queues where the output of one queue feeds one or more queues.

8 Time Reversibility Property of Irreducible, Aperiodic Markov Chains Consider a discrete time, irreducible, aperiodic Markov Chain X 1, X 2, ...... , Xn-h Xn, Xn~ 1 , ........ for which the transition probabilities are given tobe {pii}. These, for example, may arise in the study ofM/M/m type queues. The transition probabilities may be used to obtain the equilibrium state probability distribution {p;} for this chain. e. the chain ...... Xn+h Xn. .... , X 3, X 2, X 1• This would also be a Markov Chain since we can write P{Xm =jiXm+l =i,Xm+2 =iz, ......

Specifically, the mean system delay Wand queueing delay WQ may be found from this. Using Little's Result, the mean number in the system N and the mean number waiting in queue NQ may also be found for the queue in equilibrium. Note that since PASTA is applicable to this queue (the arrival process is Poisson), N and NQ will also be the average numbers (in system and waiting in queue, respectively) that an arriving customer will see. It would be interesting to find the distribution of the number in the system that will be seen by a departing customer - this would correspond to the number in the system that a customer who has just left the queuewill see, looking back into the system.

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An Introduction to Queueing Systems by Sanjay K. Bose (auth.)


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