arXiv subjects

Elijah Hradovich

Publications and source records attributed to Elijah Hradovich.

2 recordsLinked to original sources

arXiv2020

Contention resolution on a restrained channel

We examine deterministic broadcasting on multiple-access channels for a scenario when packets are injected continuously by an adversary to the buffers of the devices at rate $ρ$ packages per round. The aim is to maintain system stability, that is, bounded queues. In contrast to previous work we assume that there is a strict limit of available power, defined as the total number of stations allowed to transmit or listen to the channel at a given time, that can never be exceeded. We study how this constraint influences the quality of services with particular focus on stability. We show that in the regime of deterministic algorithms, the significance of energy restriction depends strongly on communication capabilities of broadcasting protocols. For the adaptive and full-sensing protocols, wherein stations may substantially adopt their behavior to the injection pattern, one can construct efficient algorithms using very small amounts of power without sacrificing throughput or stability of the system. In particular, we construct constant-energy adaptive and full sensing protocols stable for $ρ=1$ and any $ρ<1$, respectively, even for worst case (adversarial) injection patterns. Surprisingly, for the case of acknowledgment based algorithms that cannot adopt to the situation on the channel (i.e., their transmitting pattern is fixed in advance), limiting power leads to reducing the throughput. That is, for this class of protocols in order to preserve stability we need to reduce injection rate significantly. We support our theoretical analysis by simulation results of algorithms constructed in the paper. We depict how they work for systems of moderate, realistic sizes. We also provide a comprehensive simulation to compare our algorithms with backoff algorithms, which are common in real-world implementations, in terms of queue sizes and energy consumption.

cs.DC↗

arXiv2019

Energy Efficient Adversarial Routing in Shared Channels

We investigate routing on networks modeled as multiple access channels, when packets are injected continually. There is an energy cap understood as a bound on the number of stations that can be switched on simultaneously. Each packet is injected into some station and needs to be delivered to its destination station via the channel. A station has to be switched on in order to receive a packet when it is heard on the channel. Each station manages when it is switched on and off by way of a programmable wakeup mechanism, which is scheduled by a routing algorithm. Packet injection is governed by adversarial models that determine upper bounds on injection rates and burstiness. We develop deterministic distributed routing algorithms and assess their performance in the worst-case sense. One of the algorithms maintains bounded queues for the maximum injection rate 1 subject only to the energy cap 3. This energy cap is provably optimal, in that obtaining the same throughput with the energy cap 2 is impossible. We give algorithms subject to the minimum energy cap 2 that have latency polynomial in the total number of stations n for each fixed adversary of injection rate less than 1. An algorithm is k-energy-oblivious if at most k stations are switched on in a round and for each station the rounds when it will be switched on are determined in advance. We give a k-energy-oblivious algorithm that has packet delay O(n) for adversaries of injection rates less than (k-1)/(n-1), and show that there is no k-energy-oblivious stable algorithm against adversaries with injection rates greater than k/n. We give a k-energy-oblivious algorithm routing directly that has latency O(n^2/k) for adversaries of sufficiently small injection rates that are O(k^2/n^2). We show that no k-energy-oblivious algorithm routing directly can be stable against adversaries with injection rates greater than k(k-1)/n(n-1).

cs.DC↗