Few models in wireless communications have been addressed as thoroughly as slotted Aloha, and most important questions regarding its performance have been answered (e.g., stability). Although slotted time finite user Aloha with infinite backlog (no queueing analysis) and fixed (common) contention probability is trivial, incorporating queueing significantly increases the complexity of the problem, with a corresponding major impact on the resulting performance. The stability region of this model is known, as are many other performance aspects, but a review of the literature yields no explicit performance expressions in terms of the fundamental model parameters. This paper approximates the performance of the K coupled queues with K uncoupled geom/geom/1 queues, where the queue parameters are selected to reflect the actual coupling as closely as possible. The throughput match is excellent, and the service delay match is good. The approach can be extended to queue-specific contention probabilities in a straightforward manner.
[1]
W. Szpankowski.
Stability conditions for some distributed systems: buffered random access systems
,
1994,
Advances in Applied Probability.
[2]
A. Ephremides,et al.
Analysis, stability, and optimization of slotted ALOHA with a finite number of buffered users
,
1980,
1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.
[3]
Lang Tong,et al.
Stability and delay of finite-user slotted ALOHA with multipacket reception
,
2005,
IEEE Transactions on Information Theory.
[4]
Venkat Anantharam.
The stability region of the finite-user slotted ALOHA protocol
,
1991,
IEEE Trans. Inf. Theory.
[5]
Anthony Ephremides,et al.
On the stability of interacting queues in a multiple-access system
,
1988,
IEEE Trans. Inf. Theory.
[6]
Wei Luo,et al.
Stability of N interacting queues in random-access systems
,
1999,
IEEE Trans. Inf. Theory.