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Abstract:

We consider packet networks and make use of the "adversarial queuing theory " model [10]. We are interested in the question of guaranteeing that all packets are actually delivered to destination, and of having an upper bound on the delivery times of all packets. Whether this is possible against all rate-1 adversaries was previously posed as an open question [15, 10]. Among other, we give a queuing policy that guarantees bounded delivery time whenever the rate-1 adversary itself can deliver all packets in bounded time and adheres to certain additional conditions. On the negative side we show that even the adversary itself cannot deliver all packets in bounded time for all rate-1 sequences of packets. We thus answer the open question posed by Gamarnik [15]. We further show that delivering all packets while maintaining stability (we coin the term "reliability " for this property) can be done by an o#ine scheduler whenever the injection of packets is done at rate of at most 1. Thus any rate-1 adversary can have this property. But, on the other hand, we also show that there is no online protocol (even centralized) that can achieve that property against all rate-1 adversaries. We thus answer an open question of Borodin et al. [10].

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