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

The impacts of timing constraints on virtual channels multiplexing in interconnect networks

Interconnect networks employing wormhole-switching play a critical role in shared memory multiprocessor systems-on-chip (MPSoC) designs, multicomputer systems and system area networks. Virtual channels greatly improve the performance of wormhole-switched networks because they reduce blocking by acting as "bypass" lanes for non-blocked messages. Capturing the effects of virtual channel multiplexing has always been a crucial issue for any analytical model proposed for wormhole-switched networks. Dally has developed a model to investigate the behaviour of this multiplexing which have been widely employed in the subsequent analytical models of most routing algorithms suggested in the literature. It is indispensable to modify Dally's model in order to evaluate the performance of channel multiplexing in more general networks where restrictions such as timing constraints of input arrivals and finite buffer size of queues are common. In this paper we consider timing constraints of input arrivals to investigate the virtual channel multiplexing problem inherent in most current networks. The analysis that we propose is completely general and therefore can be used with any interconnect networks employing virtual channels. The validity of the proposed equations has been verified through simulation experiments under different working conditions