Narrow Results

We consider M/M/c/K(K ≥ c ≥ 1) retrial queues with two types of nonpersistent customers, which are motivated from modeling of service systems such as call centers. Arriving customers that see the system fully occupied either join the orbit or abandon receiving service forever. After an exponentially distributed time in the orbit, each customer either abandons the system forever or retries to occupy a server again. For the case of K = c = 1, we present an analytical solution for the generating functions in terms of confluent hypegeometric functions. In the general case, the number of customers in the system and that in the orbit form a level-dependent quasi-birth-and-death (QBD) process whose structure is sparse. Based on this sparse structure, we develop a numerically stable algorithm to compute the joint stationary distribution. We show that the computational complexity of the algorithm is linear to the capacity of the queue. Furthermore, we present a simple fixed point approximation model for the case where the algorithm is time consuming. Numerical results show various insights into the system behavior.

Call centers are service networks in which agents provide telephone-based services. An important part of call center operations is represented by service durations. In recent statistical analysis of real data, it has been noted that the distribution of service times reveals a remarkable fit to the lognormal distribution. In this paper, we discuss a possible source of this behavior by resorting to classical methods of statistical mechanics of multi-agent systems. The microscopic service time variation leading to a linear kinetic equation with lognormal equilibrium density is built up introducing as main criterion for decision a suitable value function in the spirit of the prospect theory of Kahneman and Twersky.