Fault-Tolerant Online Packet Scheduling on Parallel Channels

Abstract

We consider the problem of scheduling packets of different lengths via k directed parallel communication links. The links are prone to simultaneous errors --- if an error occurs, all links are affected. Dynamic packet arrivals and errors are modelled by a worst-case adversary. The goal is to optimize competitive throughput of online scheduling algorithms. Two types of failures are considered: jamming, when currently scheduled packets are simply not delivered, and crashes, when additionally the channel scheduler crashes losing its current state. For the former, milder type of failures, we prove an upper bound on competitive throughput of 3/4 - 1/(4k) for odd values of k, and 3/4 - 1/(4k+4) for even values of k. On constructive side, we design an online algorithm that, for packets of two different lengths, matches the upper bound on competitive throughput. To compare, scheduling on independent channels, that is, when adversary could cause errors on each channel independently, reaches throughput of 1/2. This shows that scheduling under simultaneous jamming is provably more efficient than scheduling under channel-independent jamming. In the setting with crash failures we prove a general upper bound for competitive throughput of (√5-1)/2 and design an algorithm achieving it for packets of two different lengths. This result has two interesting implications. First, simultaneous crashes are significantly stronger than simultaneous jamming. Second, due to the above mentioned upper bound of 1/2 on throughput under channel-independenterrors, scheduling under simultaneous crashes is significantly stronger than channel-independent crashes, similarly as in the case of jamming errors.