Motivated by the need for transportation infrastructure and incident management planning, we study traffic density under non-recurrent congestion. This paper provides an analytical solution approximating stationary distribution of in roadways where deterioration service occurs unpredictably. The proposed generalizes a queuing model discussed literature to long segments that are not space-homoge...

Tandem queues constitute a fundamental structure of queueing networks. However, exact queue times in tandem queues are notoriously difficult to compute except for some special cases. Several approximation schemes that are based on mathematical assumptions that enable approximate analyses of tandem queues have been reported in the literature. This article proposes an approximation approach that ...

In this paper, we consider a three-dimensional Brownian-driven tandem queue with intermediate inputs, which corresponds to semimartingale reflecting Brownian motion whose reflection matrix is triangular. For three-node queue, no closed form formula known, not only for its stationary distribution but also the corresponding transform. We are interested in exact tail asymptotics distributions. By ...

Abstract: In this article, a two-node single-processor Markovian tandem queueing system with task splitting and feedback is considered. Each node has an infinite buffer before it and, thus, no blocking is possible in the system. Splitting feature is added to the model considered and it makes it a novel tandem queue. The functional equation developed from the generating function applied to the s...

This paper presents explicit expressions for the mean sojourn times in a multi-stage tandem queue, with Poisson arrival and general service times, served by a s,ingle server with a cyclic switching rule, M/GI-G2-"'GN/l. The expressions are derived using the results of the two-stage tandem queue, M/GI-G2/1, already considered by some authors and the well-known Pollaczek-Khintchine formula. With ...

This paper studies a tandem queue with MAP inputs. A novel formulation is proposed to model it into a level-dependent quasi-birth-death process with expanding blocks. This allows us to analyze the joint time-dependent and steady-state queue length distributions efficiently. We also obtain the network sojourn time of an arbitrary customer.

A compound exponential-server timing channel consists of a number of infinite-buffer single-server queues in tandem. The message is coded in the sequence of arrival times to the first queue. We consider the performance of a structurally simple mismatch decoder that is the maximumlikelihood decoder for a single queue.

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 (two-node) 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 a...

We consider a variant of the two node tandem Jackson network where the upstream server reduces its service rate when the downstream queue exceeds some prespecified threshold. The rare event of interest is the overflow of the downstream queue. Based on a game/subsolution approach, we rigorously identify the exponential decay rate of the rare event probabilities and construct asymptotically optim...