This paper revisits a classical problem of slotted multiple access with success, idle, and collision events on each slot. First, results of a 2-user multiple access game are reported. The game was conducted at the University of Southern California over multiple semesters and involved competitions between studentdesigned algorithms. An algorithm called 4-State was a consistent winner. This algorithm is analyzed and shown to have an optimal expected score when competing against an independent version of itself. The structure of 4-State motivates exploration of the open question of how to minimize the expected time to capture the channel for a n-user situation. It is assumed that the system delivers perfect feedback on the number of users who transmitted at the end of each slot. An efficient algorithm is developed and conjectured to have an optimal expected capture time for all positive integers n. Optimality is proven in the special cases n ∈ {1, 2, 3, 4, 6} using a novel analytical technique that introduces virtual users with enhanced capabilities.
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Reversible Models for Wireless Multi-Channel Multiple Access
This paper presents a network layer model for a wireless multiple access system with both persistent and nonpersistent users. There is a single access point with multiple identical channels. Each user who wants to send a file first scans a subset of the channels to find one that is idle. If at least one idle channel is found, the user transmits a file over that channel. If no idle channel is found, a persistent user will repeat the access attempt at a later time, while a nonpersistent user will leave. This is a useful mathematical model for situations where a group of persistent users stay near an access point for an extended period of time while nonpersistent users come and go. Users have heterogeneous activity behavior, file upload rates, and service durations. The system is a complex multi-dimensional Markov chain. The steady state probabilities are found by exploiting a latent reversibility property and leveraging a discrete Fourier transform. This enables simple expressions for throughput and blocking probability.
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- Award ID(s):
- 1824418
- PAR ID:
- 10299718
- Date Published:
- Journal Name:
- IEEE Conference on Computer Communications (INFOCOM)
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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