Gordon F. Newell (auth.)'s Approximate Behavior of Tandem Queues PDF

By Gordon F. Newell (auth.)

ISBN-10: 3540095527

ISBN-13: 9783540095521

ISBN-10: 3642464106

ISBN-13: 9783642464102

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2) 1 , one encounters further complications at other edges due to the non-analytic behavior of f near edges. To avoid some of these problems, it is possible to formulate the problem in another way, which is actually more accurate than the above. One can eliminate the boundary conditions at the expense of making the diffusion equation more complicated (and almost impossible to solve explicitly). Suppose that each server is considered to be a multiple-channel server; server j has channels. In counting customers for a mul- tip Ie-channel service system, it is customary to count also the customers in service (which we have neglected in previous sections because, by implication, the number of customers in service was negligible, 0 or 1, compared with the queue).

Thus we can investigate the meaning of each boundary term individually. (t) J is near a boundary. Dk(t) to be near Dk+ l + c k+ l ' but no other The consequence of this is that the kth server might be interrupted for lack of storage in ck + l This, in itself, will have no immediate effect upon the behavior of any server except the kth. (t) J except the kth will, temporarily at least, behave as if there were no such interruption. (t) J to be close to Dk_l(t) , but no is near a boundary, the kth server may be interrupted for lack of customers.

The service rate is drastically reduced if the + queue tries to become negative or cannot dispose of served customers. 3) describes the detailed properties of the servers themselves. (t) > 0 J We will not worry as for Qj (t) > 0, These will all be minor refinements which have little effect upon the queue evolution in any situations in which one would want to use diffusion approximations. Actually the following questions will describe the behavior of the servers themselves quite accurately if the individual servers have exponential service times.

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Approximate Behavior of Tandem Queues by Gordon F. Newell (auth.)


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