On packet loss processes in high-speed networks
IEEE INFOCOM '92 Proceedings of the eleventh annual joint conference of the IEEE computer and communications societies on One world through communications (Vol. 1)
Performance of discrete-time queueing systems
Computers and Operations Research
Discrete-Time Models for Communication Systems Including ATM
Discrete-Time Models for Communication Systems Including ATM
Some algorithms for discrete time queues with finite capacity
Queueing Systems: Theory and Applications
Some algorithms for discrete time queues with finite capacity
Queueing Systems: Theory and Applications
Performance analysis of a slotted-ALOHA protocol on a capture channel with fading
Queueing Systems: Theory and Applications
Performance analysis of a fluid queue with random service rate in discrete time
ITC20'07 Proceedings of the 20th international teletraffic conference on Managing traffic performance in converged networks
| Hi-index | 0.00 |
Consider a discrete time queue with i.i.d. arrivals (see the generalisation below) and a single server with a buffer length m. Let {T}_{m} be the first time an overflow occurs. We obtain asymptotic rate of growth of moments and distributions of {T}_{m} as m \to \infty. We also show that under general conditions, the overflow epochs converge to a compound Poisson process. Furthermore, we show that the results for the overflow epochs are qualitatively as well as quantitatively different from the excursion process of an infinite buffer queue studied in continuous time in the literature. Asymptotic results for several other characteristics of the loss process are also studied, e.g., exponential decay of the probability of no loss (for a fixed buffer length) in time [0, n], as n \to \infty, total number of packets lost in [0, n], maximum run of loss states in [0, n]. We also study tails of stationary distributions. All results extend to the multiserver case and most to a Markov modulated arrival process.