  When decomposing the total orbit into $N$ sub-orbits (or simply orbits)
related to each of $N$ servers and through comparing the numbers of customers
in these orbits, we introduce a retrial supermarket model of $N$ identical
servers, where two probing-server choice numbers are respectively designed for
dynamically allocating each primary arrival and each retrial arrival into these
orbits when the chosen servers are all busy. Note that the designed purpose of
the two choice numbers can effectively improve performance measures of this
retrial supermarket model.
  This paper analyzes a simple and basic retrial supermarket model of N
identical servers, that is, Poisson arrivals, exponential service and retrial
times. To this end, we first provide a detailed probability computation to set
up an infinite-dimensional system of differential equations (or mean-field
equations) satisfied by the expected fraction vector. Then, as N goes to
infinity, we apply the operator semigroup to obtaining the mean-field limit (or
chaos of propagation) for the sequence of Markov processes which express the
state of this retrial supermarket model. Specifically, some simple and basic
conditions for the mean-field limit as well as for the Lipschitz condition are
established through the first two moments of the queue length in any orbit.
Finally, we show that the fixed point satisfies a system of nonlinear equations
which is an interesting networking generalization of the tail equations given
in the M/M/1 retrial queue, and also use the fixed point to give performance
analysis of this retrial supermarket model through numerical computation.
