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Abstract
This paper studies M/M/$c$/$c$ retrial queues, where $c$ servers are
all identical. In the retrial queues, an arriving customer is served
immediately if it finds an idle server upon arrival, otherwise the
customer tries to enter the system after an exponentially distributed
time independently of other customers. As is well known, it is a
challenging problem to obtain an analytical solution for the stationary
joint distribution of the numbers of retrial customers and busy
servers in the M/M/$c$/$c$ retrial queue especially for $c \ge
3$. Under some technical assumptions, a few analytical solutions have
been presented for $c \ge 3$. This paper derives analytical solutions
for M/M/3/3 and M/M/4/4 retrial queues without such technical
assumptions. Through many numerical examples, we show that the derived
analytical solutions can be computed by a numerically stable
algorithm.
Mathematics Subject Classification: Primary: 68M20, 90B22; Secondary: 60K25.
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