相关论文: On Mixed Time-Changed Erlang Queue
Experimental observations of typical kinds of synchronization transitions are reported in unidirectionally coupled time-delay electronic circuits with a threshold nonlinearity and two time delays, namely feedback delay $\tau_1$ and coupling…
The Erlang loss formula, also known as the Erlang B formula, has been known for over a century and has been used in a wide range of applications, from telephony to hospital intensive care unit management. It provides the blocking…
Compartmental ordinary differential equation (ODE) models are used extensively in mathematical biology. When transit between compartments occurs at a constant rate, the well-known linear chain trick can be used to show that the ODE model is…
This paper studies the moment boundedness of solutions of linear stochastic delay differential equations with distributed delay. For a linear stochastic delay differential equation, the first moment stability is known to be identical to…
Queueing networks are systems of theoretical interest that find widespread use in the performance evaluation of interconnected resources. In comparison to counterpart models in genetics or mathematical biology, the stochastic (jump)…
We study the impact of competing time delays in coupled stochastic synchronization and coordination problems. We consider two types of delays: transmission delays between interacting elements and processing, cognitive, or execution delays…
Recent studies indicate that in many situations service times are affected by the experienced queueing delay of the particular customer. This effect has been detected in different areas, such as health care, call centers and…
In this paper we consider a system with two carousels operated by one picker. The items to be picked are randomly located on the carousels and the pick times follow a phase-type distribution. The picker alternates between the two carousels,…
We consider continuous-time Markov chains on integers which allow transitions to adjacent states only, with alternating rates. We give explicit formulas for probability generating functions, and also for means, variances and state…
In this paper, we analyze a multiserver Markovian queue with customer abandonment i.e. the Erlang-A queue uder a novel framework, i.e. the random impulsive differential equations (RIDEs). This framework captures systems that evolve…
We consider an extension of the standard G/G/1 queue, described by the equation $W\stackrel{\mathcal{D}}{=}\max\{0, B-A+YW\}$, where $\mathbb{P}[Y=1]=p$ and $\mathbb{P}[Y=-1]=1-p$. For $p=1$ this model reduces to the classical Lindley…
We consider a single-server queue where interarrival and service times depend linearly and randomly on customer waiting times, and establish a sample-path moderate deviation principle (MDP) for the waiting time process. The waiting times…
We focus on a particular connection between queueing and risk models in a multi-dimensional setting. We first consider the joint workload process in a queueing model with parallel queues and simultaneous arrivals at the queues. For the case…
We analyze the time-dependent behavior of an $M/M/c$ priority queue having two customer classes, class-dependent service rates, and preemptive priority between classes. More particularly, we develop a method that determines the Laplace…
Since the complexity of the practical environment, many distributed networked systems can not be illustrated with the integer-order dynamics and only be described as the fractional-order dynamics. Suppose multi-agent systems will show the…
Delayed processes are ubiquitous in biological systems and are often characterized by delay differential equations (DDEs) and their extension to include stochastic effects. DDEs do not explicitly incorporate intermediate states associated…
We study a discrete time queueing system where deterministic arrivals have i.i.d. exponential delays $\xi_{i}$. The standard deviation $\sigma$ of the delay is finite, but its value is much larger than the deterministic unit service time.…
Statistical static timing analysis deals with the increasing variations in manufacturing processes to reduce the pessimism in the worst case timing analysis. Because of the correlation between delays of circuit components, timing model…
In this work, we focus on the stationary analysis of a specific class of continuous time Markov-modulated reflected random walks in the quarter plane with applications in the modelling of two-node Markov-modulated queueing networks with…
The continuous time random walk model plays an important role in modeling of so called anomalous diffusion behaviour. One of the specific property of such model are constant time periods visible in trajectory. In the continuous time random…