Mixed policies for online job allocation in one class of systems with parallel service

Consideration is given to the problem of efficient job allocation in the class of systems with parallel service on independently working single-server stations each equipped with the infinite capacity queue. There is one dispatcher which routes jobs, arriving one by one, to servers. The dispatcher does not have a queue to store the jobs and, thus, the routing decision must be made on the fly. No jockeying between servers is allowed and jobs cannot be rejected. For a job, there is the soft deadline (maximum waiting time in the queue). If the deadline is violated, a fixed cost is incurred and the job remains in the system and must be served. The goal is to find the job allocation policy which minimizes both the job's stationary response time and probability of job's deadline violation. Based on simulation results, it is demonstrated that the goal may be achieved (to some extent) by adopting a mixed policy, i.e. a proper dispatching rule and the service discipline in the server.