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REMARK 10.4.7. The main examples when the conditions of this de nition are satis ed (i.e., Gartner Ellis conditions hold) are nite state space Markov chains or processes. Also, in terms of the on=off processes the conditions will hold whenever the distribution of on periods is exponentially bounded and off periods have a nite mean. Recall that F and F1 represent the distribution and the integrated tail distribution, respectively, of an on period. Then, we arrive at the following result (see Jelenkovic and Lazar [35]). Theorem 10.4.8. Consider a single server queue with a capacity c, and two independent arrival streams et and at . Assume that et is an exponential process and at is an on=off process with rate r, F P ir, and generally distributed off periods def with a nite mean. If E et at < c, r > cH c Eet , then the queue asymptotics of this queueing system is equal to the queue asymptotics in which only the on=off process arrives and the server capacity is replaced by cH, that is, it is given by Eq. (10.16) in which c is replaced by cH. REMARK 10.4.9. This result is true with exactly the same proof if the assumption of 0 et being exponential is replaced with P supt!0 t eu c du > x o F1 x , for all c > Eet . HEURISTIC 10.4.10. Large buildups in this uid queue occur due to long and isolated on periods in at . During these long on periods the uctuations in the exponential arrival stream et average out, and therefore its contribution to the asymptotic behavior is only through its mean value.

Copyright 1999 Gary McGraw and Edward Felten. All rights reserved. Published by John Wiley & Sons, Inc.

The problem of multiplexing on=off sources arises frequently as the basic model of contention in multimedia communication systems, as well as in some storage systems. The analysis of this problem dates back to Rubinovitch [53] and Cohen [21]. Cohen obtained a complete Laplace transform solution to this problem.

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However, inverting the Laplace transform is usually a very tedious process Hence, computationally tractable exact and approximate solution techniques are needed For Markovian ( uid) on=off processes a thorough investigation of this problem was done in Anick et al [3] Many other results for multiplexing Markovian on=off processes followed These led to the equivalent bandwidth theory for Markovian (or in general exponentially bounded) arrival processes; extensive references can be found in Duf eld and O'Connell [24], Elwalid et al [25], and Glynn and Whitt [26] The analysis of a uid queue in which more than one long-tailed process is multiplexed appears to be a very dif cult problem This is due to the fact that the renewal structure of an aggregate arrival process may be very complex, although the appearance of each individual process may be truly innocuous (like an on=off process).

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The complex autocorrelation structure of the aggregate process obtained by multiplexing long-tailed on=off processes has been examined in Heath et al [28] General bounds for multiplexing long-tailed uid processes have been derived in Choudhury et al [16] In Poisson scaling the limiting case of an in nite number of on=off processes converges to the so-called M =GI =I process Asymptotic results for a uid queue with a heavy-tailed M=GI =I arrival process have been obtained in Boxma [12, 13] and Jelenkovic and Lazar [35] Recently, new results on this model have been derived in Heath et al [29] and Resnick and Samorodnitsky [50] For various bounds in this context see Nain et al [46] 10431 Activity Period of an M=GI=I Process Let Tn ; n ! 0; I < n < I, be a stationary Poisson process with rate L.

by Ryan A. MacMichael A little under ten years ago, there was a company betting their livelihood on the popularity of electronic books. They put out a handheld device that cost a few hundred dollars and offered e-books and emagazines on disk. This was before the Internet had become a household necessity and the idea did not go over very well at all -- they disappeared in less than a year. Why did they go under For some of the obvious reasons: poor screen resolution, the general clunkiness of the reader, and it just didn't feel right needing batteries to read a book at the beach. It was pretty clear then that electronic books were not going to be a serious competitor to the physical book anytime soon. Cliff Stoll felt much the same way, as he talked at length about in Silicon Snake Oil: Second Thoughts on the Information Highway. I'd say, unequivocally, that the world is not ready for a handheld device like the one above to out-and-out replace the physical book. However, with the extreme popularity of the Web, the release of an online book is a wonderful complement to the release its physical counterpart:

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