A queueing-theoretic model for resource allocation in one-dimensional distributed analytics network?

We consider the problem of allocating requesters of analytic tasks to resources on servers. We assume both requesters and servers are placed in a one dimensional line: [0,1) according to two Poisson processes with each server having finite capacity. Requesters communicate with servers under a noninterference wireless protocol. We consider a "Move to Right" (MTR) request allocation strategy where each requester is allocated to the nearest available server to its right. We start our analysis from a single resource per request scenario where each requester demands a single computational resource. We map this scenario to an M/M/1 queue or a bulk service M/M/1 queue depending on the server capacity. We compare the performance of the MTR strategy with the globally optimal strategy taking "expected distance traveled by a request" (request distance) as performance metric. Next, we extend our analysis to two resources per request scenario. We show that the behavior of MTR can be transformed into an equivalent fork-join queue problem. Numerical results are presented to validate the claim.