Admission control for service systems with impatient customers: Value of information

We consider the admission control problem in an M/M/s+G queueing system, where the arrival process is Poisson, service times are i.i.d. exponential, there are s servers and the customers have random impatience times. A customer whose queueing time exceeds his impatience time leaves the system without getting served. The system earns a unit reward from serving a customer if the customer gets served and it costs h dollars to keep a customer waiting for service for one unit of time, regardless of whether the customer gets served. We study optimal admission control policies that maximize the long run net revenue (reward-cost) per unit time under two cases: partial information (where we only know the number of customers in the system) and full information (where we know the virtual queueing time, VQT). We show that a VQT based threshold policy is optimal in the full information case if the impatience times are constant. We use numerical computation and simulation to observe that the maximum value of using full information over partial information is fairly insensitive to the impatience time and service time distributions. Thus we can replace the M/G/s+G system by an equivalent M/M/s+M system with the same mean service times and impatience times, and use the resulting queue-length based optimal policies as excellent approximations. We validate these conclusions by using real data from a call center of a US bank.