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In a multi-server system, how can one get better performance than randomassignment of jobs to servers if queue-states cannot be queried by thedispatcher? A replication strategy has recently been proposed where $d$ copiesof each arriving job are sent to servers chosen at random. The job's completiontime is the first time that the service of any of its copies is complete. Oncompletion, redundant copies of the job are removed from other queues so as notto overburden the system.  For digital jobs, where the objects to be served can be algebraicallymanipulated, and for servers whose output is a linear function of their input,here we consider an alternate strategy: Maximum Distance Separable (MDS) codes.For every batch of $n$ digital jobs that arrive, $n+m$ linear combinations arecreated over the reals or a large finite field, and each coded job is sent to arandom server. The batch completion time is the first time that any $n$ of the$n+m$ coded jobs are served, as the evaluation of $n$ original jobs can berecovered by Gaussian elimination. If redundant jobs can be removed from queueson batch completion, we establish that in order to get the improvedresponse-time performance of sending $d$ copies of each of $n$ jobs via thereplication strategy, with the MDS methodology it suffices to send $n+d$ jobs.That is, while replication is multiplicative, MDS is linear.

MDS coding is better than replication for job completion times