Analysis of an M/G/1 queue with customer impatience and an adaptive arrival process

We study an M/G/1 queue with impatience and an adaptive arrival process. The rate of the arrival process changes according to whether an incoming customer is accepted or rejected. We analyse two different models for impatience : (i) based on workload, and (ii) based on queue length. For the workload-based model, we obtain the Laplace-Stieltjes Transform of the joint stationary workload and arrival rate process, and that of the waiting time. For the queue-length based model we obtain the analogous z-transform. These queueing models also capture the interaction between congestion control algorithms and queue management schemes in the Internet

Performance analysis of a discrete-time queueing system with customer deadlines

This paper studies a discrete-time queueing system where each customer has a maximum allowed sojourn time in the system, referred to as the "deadline" of the customer. Deadlines of consecutive customers are modelled as independent and geometrically distributed random variables. The arrival process of new customers, furthermore, is assumed to be general and independent, while service times of the customers are deterministically equal to one slot each. For this queueing model, we are able to obtain exact formulas for quantities as the mean system content, the mean customer delay, and the deadline-expiration ratio. These formulas, however, contain infinite sums and infinite products, which implies that truncations are required to actually compute numerical values. Therefore, we also derive some easy-to-evaluate approximate results for the main performance measures. These approximate results are quite accurate, as we show in some numerical examples. Possible applications of this type of queueing model are numerous: the (variable) deadlines could model, for instance, the fact that customers may become impatient and leave the queue unserved if they have to wait too long in line, but they could also reflect the fact that the service of a customer is not useful anymore if it cannot be delivered soon enough, etc

Holistic assessment of call centre performance

In modern call centres 60–70% of the operational costs come in the form of the human agents who take the calls. Ensuring that the call centre operates at lowest cost and maximum efficiency involves a trade‐off of the cost of agents against lost revenue and increased customer dissatisfaction due to lost calls. Modelling the performance characteristics of a call centre in terms of the agent queue alone misses key performance influencers, specifically the interaction between channel availability at the media gateway and the time a call is queued. A blocking probability at the media gateway, as low as 0.45%, has a significant impact on the degree of queuing observed and therefore the cost and performance of the call centre. Our analysis also shows how abandonment impacts queuing delay. However, the call centre manager has less control over this than the level of contention at the media gateway. Our commercial assessment provides an evaluation of the balance between abandonment and contention, and shows that the difference in cost between the best and worst strategy is £130K per annum, however this must be balanced against a possible additional £2.98 m exposure in lost calls if abandonment alone is used