The scope of this work is twofold: On the one hand, strongly motivated by emerging engineering issues in multiple access communication systems, we investigate the performance of a slotted-time relay-assisted cooperative random access wireless network with collisions and with join the shortest queue relay-routing protocol. For this model, we investigate the stability condition, and apply different methods to derive the joint equilibrium distribution of the queue lengths. On the other hand, using the cooperative communication system as a vehicle for illustration, we investigate and compare three different approaches for this type of multi-dimensional stochastic processes, namely the compensation approach, the power series algorithm (PSA), and the probability generating function (PGF) approach. We present an extensive numerical comparison of the compensation approach and PSA, and discuss which method performs better in terms of accuracy and computation time. We also provide details on how to compute the PGF in terms of a solution of a Riemann-Hilbert boundary value problem.
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