On the large deviations of resequencing queue size: 2-M/M/1 case

In data communication networks, packets that arrive at the receiving host may be disordered for reasons such as retransmission of dropped packets or multipath routing. Reliable protocols such as the Transmission Control Protocol (TCP) require packets to be accepted, i.e., delivered to the receiving application, in the order they are transmitted at the sender. In order to do so, the receiver's transport layer is responsible for temporarily buffering out-of-order packets and resequencing them as more packets arrive. In this paper, we analyze a model where the disordering is caused by multipath routing. Packets are generated according to a Poisson process. Then, they arrive at a disordering network (DN) modeled by two parallel M/M/1 queues, and are routed to each of the queues according to an independent Bernoulli process. A resequencing buffer follows the DN. In such a model, the packet resequencing delay is known. However, the size of the resequencing queue (RSQ) is unknown. We derive the probability for the large deviations of the queue size.