In this paper, we refine the calculus proposed in [5, 8, 91. The new calculus, including network operations for multiplexing, input-output relation, and routing, allows us to compute tighter exponential bounds for the tail distributions of queue lengths in intree networks with routing. In particular, if external arrival processes and routing processes are either Markov arrival processes or auto...

We develop a queueing model for an appointment-based service system that consists of two queues in tandem: the appointment queue followed by the service queue. Customers join the appointment queue when they call for appointments, stay there (not physically) until the appointment time comes, and then leave the appointment queue and may physically join the service queue, and wait there until serv...

Considering impatient users in space information networks, a preliminary queue congestion control model was presented. It balanced the network loads and make up for the resource lost from the impatient leaving users. To describe the competition among nodes, the model used queuing game theory. The introduced congestion control platform, which consisted of service nodes, calculated user’s gain to...

An approximation algorithm is presented for open tandem queueing networks with finite buffers and with general service times. The algorithm decomposes the system into individual queues with revised arrival and service process and revised queue capacity. Then, each queue is analyzed in isolation. The service process is revised so that to reB.ect the additional delay a unit might undergo due to b...

In this paper, we consider a PH/M/2 queue in which each server has its own queue and arriving customers join the shortest queue. For this model, it has been conjectured that the decay rate of the tail probabilities for the shortest queue length in the steady state is equal to the square of the decay rate for the queue length in the corresponding PH/M/2 model with a single queue. We prove this f...

In many real life queueing systems, customer balk from the queue but the environment is aware of it only at their times to be served. Naturally, the balking is an outcome of the queue length, and the decision is based on a threshold. Yet, the inspected queue length contains customers who balked In this work, we consider a Markovian queue with infinite capacity with homogeneous customers with re...

In a communication network, asymptotic quality of service metrics specify the probability that the delay or buffer occupancy becomes large. An understanding of these metrics is essential for providing worst-case delay guarantees, provisioning buffer sizes in networks, and to estimate the frequency of packet-drops due to buffer overflow. Second, many network control tasks utilize queue length in...