Related papers: Sample path large deviations for multiclass feedfo…

We investigate a computer network consisting of two layers occurring in, for example, application servers. The first layer incorporates the arrival of jobs at a network of multi-server nodes, which we model as a many-server Jackson network.…

We consider an infinite-server queue into which customers arrive according to a Cox process and have independent service times with a general distribution. We prove a functional large deviations principle for the equilibrium queue length…

In this paper we present a queueing network approach to the problem of routing and rebalancing a fleet of self-driving vehicles providing on-demand mobility within a capacitated road network. We refer to such systems as autonomous…

We establish heavy traffic limit theorems for queue-length processes in critically loaded single class queueing networks with state dependent arrival and service rates. A distinguishing feature of our model is non-Markovian state…

This paper studies the heavy-traffic (HT) behaviour of queueing networks with a single roving server. External customers arrive at the queues according to independent renewal processes and after completing service, a customer either leaves…

Arrival processes to service systems often display fluctuations that are larger than anticipated under the Poisson assumption, a phenomenon that is referred to as overdispersion. Motivated by this, we analyze a class of discrete stochastic…

Discrete-time queueing system has widespread applications in packet switching networks, internet protocol, Broadband Integrated Services Digital Network (B-ISDN), circuit switched time-division multiple access etc. In this paper, we analyze…

This paper focuses on systems of nonlinear second-order stochastic differential equations with multi-scales. The motivation for our study stems from mathematical physics and statistical mechanics, for examples, Langevin dynamics and…

One-dimensional run-and-tumble processes may converge towards some localized non-equilibrium steady state when the two velocities and/or the two switching rates are space-dependent. A long dynamical trajectory can be then analyzed via the…

The presented study elaborates a multi-server priority queueing model considering the pre-emptive repeat policy and phase-type distribution (PH) for retrial process. The incoming heterogeneous calls are categorized as handoff calls and new…

While suitably scaled CNNs with Gaussian initialization are known to converge to Gaussian processes as the number of channels diverges, little is known beyond this Gaussian limit. We establish a large deviation principle (LDP) for…

We consider the problem of scheduling a queueing system in which many statistically identical servers cater to several classes of impatient customers. Service times and impatience clocks are exponential while arrival processes are renewal.…

A broad class of parallel server systems is considered, for which we prove the steady-state asymptotic independence of server workloads, as the number of servers goes to infinity, while the system load remains sub-critical. Arriving jobs…

We prove a Large Deviation Principle for {\color{blue} jump-Markov } Processes on sparse large disordered network with disordered connectivity. The network is embedded in a geometric space, with the probability of a connection a (scaled)…

The single server queue with multiple customer types and semi-Markovian service times, sometimes referred to as the $M/SM/1$ queue, has been well-studied since its introduction by Neuts in 1966. In this paper, we apply an extension of this…

We analytically evaluate the large deviation function in a simple model of classical particle transfer between two reservoirs. We illustrate how the asymptotic large time regime is reached starting from a special propagating initial…

We obtain the posterior distribution of a random process conditioned on observing the empirical frequencies of a finite sample path. We find under a rather broad assumption on the "dependence structure" of the process, {\em c.f.}…

This paper studies an infinite-server queue in a random environment, meaning that the arrival rate, the service requirements and the server work rate are modulated by a general c\`{a}dl\`{a}g stochastic background process. To prove a large…

We propose an analytical technique to study large fluctuations and switching from internal noise in complex networks. Using order-disorder kinetics as a generic example, we construct and analyze the most probable, or optimal path of…

There is a wide variety of message-passing communication models, ranging from synchronous ''rendez-vous'' communications to fully asynchronous/out-of-order communications. For large-scale distributed systems, the communication model is…