Delay analysis of a dynamic queue-based random access network
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Motivated by design and performance challenges stemming from emerging applications in random-access networks, we focus on the performance of a dynamic two-user slotted-time ALOHA network with a general queue-dependent transmission policy. At the beginning of each slot, each user transmits a packet with a probability that depends on the number of stored packets at both user queues. If both stations transmit at the same slot a collision occurs, and both packets must be retransmitted in a later slot. Each user has external bursty arrivals that are stored in their infinite capacity queues. Arrival processes are independent of each other, but depend also on the state of the network at the beginning of a slot. In such a network of interacting queues, when a user transmits a packet, it causes interference to the nearby user and decreases its rate of communication. Each user is aware of the status of the network, and accordingly reconfigures its transmission parameters to improve the network performance. We investigate the ergodicity conditions and use the generating function approach to investigate the queueing delay. Generating functions for the steady-state distribution are obtained by solving a finite system of linear equations and a functional equation with the aid of the theory of Riemann-Hilbert boundary value problems.
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