A queueing system (M/G1,G2/1/K) is considered in which the service time
of a customer entering service depends on whether the queue length, N(t),
is above or below a threshold L. The arrival process is Poisson, and the
general service times S1 and S2 depend on whether the queue length at the
time service is initiated is <L or ≥L, respectively. Balance equations
are given for the stationary probabilities of the Markov process (N(t),X(t)), where X(t) is the remaining service time of the customer currently
in service. Exact solutions for the stationary probabilities are constructed
for both infinite and finite capacity systems. Asymptotic approximations
of the solutions are given, which yield simple formulas for performance
measures such as loss rates and tail probabilities. The numerical accuracy
of the asymptotic results is tested.