Dynamic load allocation in parallel queues with synchronisation

The dynamic optimization problem of allocating incoming messages into K parallel queues is considered when the interarrival times and the workloads of the messages form two independent renewal sequences. Upon arrival, messages are broken into L⩽K (1⩽L⩽K) smaller packets and queued in parallel buffers for transmission over channels of fixed and equal capacity. At the destination, the messages are resequenced after reassembly. The problem is formulated as a Markov decision problem, where the cost per stage is taken as the end-to-end delay of each message, including the synchronization delays, due to reassembly and resequencing. It is shown that the optimal policy allocates the message workload to the queues so as to drive the workload in each queue into a balanced configuration as fast as feasible. A simple algorithm that computes the optimal allocation vector is provided