A discrete-time queue with customers with geometric 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. More specifically, we model the deadlines of the consecutive customers as independent and geometrically distributed random variables. Customers enter the system according to a general independent arrival process, i.e., the numbers of arrivals during consecutive time slots are i.i.d. random variables with arbitrary distribution. Service times of the customers are deterministically equal to one slot each. For this queueing model, we are able to obtain exact formulas for such quantities as the generating function and the expected value of the 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 app...

• Type: Journal
• Year: 2015
• Where: PE
• Authors: Herwig Bruneel, Tom Maertens
• Keywords: Optimization, PE 2015