The impact of bursty traffic on queues is investigated in this paper. We consider a discrete-time single server queue with
an infinite storage room, that releases customers at the constant rate of
c customers/slot. The queue is fed by an M/G/∞ process. The M/G/∞ process can be seen as a process resulting from the superposition
of infinitely many ‘sessions’: sessions become active according to a Poisson process; a station stays active for a random
time, with probability distribution
G, after which it becomes inactive. The number of customers entering the queue in the time-interval [
t,
t + 1) is then defined as the number of active sessions at time
t (
t = 0,1, ...) or, equivalently, as the number of busy servers at time
t in an M/G/∞ queue, thereby explaining the terminology. The M/G/∞ process enjoys several attractive features: First, it can
display various forms of dependencies, the extent of which being governed by the service time distribution
G. The heavier the tail of
G, the more bursty the M/G/∞ process. Second, this process arises naturally in teletraffic as the limiting case for the aggregation
of on/off sources [27]. Third, it has been shown to be a good model for various types of network traffic, including telnet/ftp
connections [37] and variable-bit-rate (VBR) video traffic [24]. Last but not least, it is amenable to queueing analysis due
to its very strong structural properties. In this paper, we compute an asymptotic lower bound for the tail distribution of
the queue length. This bound suggests that the queueing delays will dramatically increase as the burstiness of the M/G/∞ input
process increases. More specifically, if the tail of
G is heavy, implying a bursty input process, then the tail of the queue length will also be heavy. This result is in sharp
contrast with the exponential decay rate of the tail distribution of the queue length in presence of ‘non-bursty’ traffic
(e.g. Poisson-like traffic).
This revised version was published online in August 2006 with corrections to the Cover Date.
相似文献