This paper considers Gaussian flows multiplexed in a queueing network. A single node being a useful but often incomplete setting, we examine more advanced models. We focus on a (twonode) tandem queue, fed by a large number of Gaussian inputs. With service rates and buffer sizes at both nodes scaled appropriately, Schilder’s sample-path large deviations theorem can be applied to calculate the as...

Consider the single server queue with an infinite buffer and a FIFO discipline, either of type M/M/1 or Geom/Geom/1. Denote by A the arrival process and by s the services. Assume the stability condition to be satisfied. Denote by D the departure process in equilibrium and by r the time spent by the customers at the very back of the queue. We prove that (D, r) has the same law as (A, s) which is...

In this paper we study single-server tandem queues with general service times and finite buffers. Jobs are served according to the Blocking-After-Service protocol. To approximately determine the throughput and mean sojourn time, we decompose the tandem queue into single-buffer subsystems, the service times of which include starvation and blocking, and then iteratively estimate the unknown param...

Consider the single server queue with an infinite buffer and a FIFO discipline, either of type M/M/1 or Geom/Geom/1. Denote by A the arrival process and by s the services. Assume the stability condition to be satisfied. Denote by D the departure process in equilibrium and by r the time spent by the customers at the very back of the queue. We prove that (D, r) has the same law as (A, s) which is...

We consider a tandem queue with coupled processors and analyze the two-dimensional Markov process representing the numbers of jobs in the two stations. A functional equation for the generating function of the stationary distribution of this two-dimensional process is derived and solved through the theory of Riemann-Hilbert boundary value problems.

This paper considers importance sampling as a tool for rareevent simulation. The focus is on estimating the probability of overflow in the downstream queue of a Jackson twonode tandem queue. It is known that in this setting ‘traditional’ state-independent importance-sampling distributions perform poorly. We therefore concentrate on developing a state-dependent change of measure that is provably...

We first consider a single–server queue that serves a tagged MMPP–2 stream and a background MMPP–2 stream in a FIFO manner. The service time is exponentially distributed. For this queueing system, we obtain the CDF of the tagged inter-departure time, from which we can calculate the jitter, defined as a percentile of the inter–departure time. The formulation is exact, but the solution is obtaine...

Consider the single server queue with an infinite buffer and a FIFO discipline, either of type M M 1 or Geom/Geom/1. Denote by A the arrival process and by s the services. Assume the stability condition to be satisfied. Denote by D the departure process in equilibrium and by r the time spent by the customers at the very back of the queue. We prove that D r has the same law as A s which is an ex...

In this paper, we will develop a tool to analyze polling systems with the autonomous-server, the time-limited, and the k-limited service discipline. It is known that these disciplines do not satisfy the well-known branching property in polling system, therefore, hardly any exact result exists in the literature for them. Our strategy is to apply an iterative scheme that is based on relating in c...

We consider an infinite tandem of first-come-first-served queues. The service times have unit mean, and are independent and identically distributed across queues and customers. Let I be a stationary and ergodic interarrival sequence with marginals of mean τ > 1, and suppose it is independent of all service times. The process I is said to be a fixed point for the first, and hence for each, queue...