In this paper we study a broad class of semi-Markovian queues introduced by Sengupta. This class contains many classical queues such as the GI/M/1 queue, SM/MAP/1 queue and others, as well as queues with correlated inter-arrival and service times. Queues belonging to this class are characterized by a set of matrices of size m and Sengupta showed that its waiting time distribution can be represe...

We derive the performance measures for non-priority customers in a priority single-server queue with two types of Markovian arrival processes (MAPs). One type of customers has preemptive resume (or repeat) priority over the other. We regard the model with two types of MAP arrivals as an MAP/SM/l queue with only non-priority customers arrivals, semi-Markovian service times and some server vacati...

Consider a single server queue in which the service station may breakdown according to a Poisson process with rates γ in busy time and γ’ in idle time respectively. After a breakdown, the service station will be repaired immediately and the repair time is assumed to have an exponential distribution with rate δ. Suppose the arrival time has an exponential distribution with rate λ, and the probab...

We consider the FCFS GI/GI/n queue in the so-called HalfinWhitt heavy traffic regime. We prove that under minor technical conditions the associated sequence of steady-state queue length distributions, normalized by n 1 2 , is tight. We derive an upper bound on the large deviation exponent of the limiting steady-state queue length matching that conjectured by Gamarnik and Momcilovic in [16]. We ...

The present paper deals with the problem of calculating queue length distributions in a polling model with (exhaustive) limited service under the assumption of general arrival, service and setup distributions. The interest for this model is fueled by an application in the field of logistics. Knowledge of the queue length distributions is needed to operate the system properly. The multi-queue po...

We study a single-server queue, operating under the first-in-first-out (FIFO) service discipline, in which each customer independently abandons the queue if his service has not begun within a generally distributed amount of time. Under some mild conditions on the abandonment distribution, we identify a limiting heavy-traffic regime in which the resulting diffusion approximation for both the off...

We consider traffic dynamics for a network of signalized intersections under fixed time control, where the outflow from every link is constrained to be equal to an autonomous capacity function (and hence fixed-time control) if the queue length is positive and equal to the cumulative inflow otherwise. In spite of the resulting dynamics being nonLipschitz, recent work has shown existence and uniq...

Queue length is an important parameter for traffic-signal priority systems emergency vehicles. Instead of using conventional detector data, this paper investigates the feasibility queue-length estimation Google Maps color-code data via random forest (RF) and gradient-boosting machine (GBM) methods. Alternative ways specifying independent variables from are also investigated. Additionally, model...

A single server commences its service at time zero every day. random number of customers decide when to arrive the system so as minimize waiting and tardiness costs. The costs are proportional with rates $$\alpha $$ $$\beta , respectively. Each customer’s optimal arrival depends on others’ decisions; thus, resulting strategy is a Nash equilibrium. This work considers estimation ratio $$\display...