Analysis of the resequencing buffer in a homogeneous M/M/2 queue

The resequencing problem is encountered in many practical information systems such as distributed database and communication networks. In these systems customers, such as messages in a computer network, have to be delivered to users in their original order. Therefore, those customers which become out of order due to the randomness of the system are forced to wait in a resequencing buffer so that their delivered order can be guaranteed. The previous work on the resequencing problem mainly concentrated on the delay aspect. From both theoretical and practical viewpoints, however, the queue length characteristics of the resequencing buffer are also significant. We consider the queue length distribution of the resequencing buffer fed by a homogeneous M/M/2 queue. The exact analysis is carried out for the probability mass functions of the queue length in equilibrium and the maximal occupancy which corresponds to the queue length just before the departure instants of customers from the resequencing buffer.