Competitive queueing policies for QoS switches

We consider packet scheduling in a network providing differentiated services, where each packet is assigned a value. We study various queueing models for supporting QoS (Quality of Service). In the nonpreemptive model, packets accepted to the queue will be transmitted eventually and cannot be dropped. The FIFO preemptive model allows packets accepted to the queue to be preempted (dropped) prior to their departure, while ensuring that transmitted packets are sent in the order of arrival. In the bounded delay model, packets must be transmitted before a certain deadline, otherwise it is lost (while transmission ordering is allowed to be arbitrary). In all models the goal of the buffer policy is to maximize the total value of the accepted packets.Let α be the ratio between the maximal and minimal value. For the non-preemptive model we derive a Θ(log &alpha) competitive ratio, both exhibiting a buffer policy and a general lower bound. For the interesting case of two distinct values, we give an 2α--1/α competitive buffer policy, which exactly matches the lower bound. We also analyze a RED-like policy and derive its competitive ratio, which is approximately 2α--0.5/α for two values and Θ(log α) for multiple values. In addition we improve the previous known lower and upper bounds of the Fixed Partition and Flexible Partition policies.For the FIFO preemptive model, we improve the general lower bound and show a tight bound for the special case of queue size 2. We prove that the bounded delay model with uniform delay 2 is equivalent to a modified FIFO preemptive model with queue size 2. We then give improved upper and lower bounds on the 2-uniform bounded delay model. We also give lower bound for the 2-variable bounded delay model, which matches the previously known upper bound.