A Single Channel on - off Communication Model

1.1 INTRODUCTION There now exist several large teletraac data sets exhibiting non-standard features incompatible with classical assumtions of short range dependence and rapidly decreasing tails. For instance, it is worth exploring the variety of data catalogued at the ITA web site www.acm.org/sigcomm/ITA/. These data sets exhibit the phenomena of heavy-tailed marginal distributions and long range dependence. Tails can be so heavy that only innnite variance models are possible (eg, 43]), and sometimes, as in le size data, even rst moments are innnite. See 1]. Heavy tails have been t to le lengths ((1], 9],,10]) cpu time to complete a job, call holding times, inter-arrival times between packets in a network ((39]), lengths of on/oo cycles ((43], 42]). Other areas where heavy tails abound are nance and economics ((12], 13], 20], 6], 7]) and insurance analysis ((30], 32]). Of course, long range dependence was originially considered in hydrology in connection with the Hurst phenomenon. See 21], 22], 4], 5]. In telecommunications, long range dependence has been found in video conference data (3]), packet counts per unit time in ethernet traac ((27]) and in bytes per unit time in WWW traac ((9], 10]).