Flows with Bounded Waiting Time in Networked and Distributed Systems

Many real world situations involve queueing systems in which customers renege (leave the queue after entering) according to a given distribution. We consider a system with a single deterministic server and FCFS scheduling discipline. Customer interarrival times are distributed exponentially. Each arriving customer is limited to a deterministically distributed patience time after which it must depart the system, and is considered lost. We present an insightful model to calculate the average number of customers in a reneging system using a related queueing system in which customers balk (refuse to join the queue) with a probability. Then, we derive expressions to calculate the probabilities of the number of customers in a balking system. Using these probabilities, we provide useful results such as calculation of jitter and average degree of multiplexing. Simulation experiments under different working conditions verify the validity of the proposed equations