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Collision models describe the sequential interactions of a system with independent ancillas. Motivated by recent advances in neutral atom arrays, in this Letter we investigate a model where the ancillas are governed by a classical…
We study networks of interacting queues governed by utility-maximising service-rate allocations in both discrete and continuous time. For {\em finite} networks we establish stability and some steady-state moment bounds under natural…
In this paper, we focus on the implementation of distributed programs in using a key-value store where the state of the nodes is stored in a replicated and partitioned data store to improve performance and reliability. Applications of such…
Modeling joint probability distributions over sequences has been studied from many perspectives. The physics community developed matrix product states, a tensor-train decomposition for probabilistic modeling, motivated by the need to…
We revisit the classic Cournot model and extend it to a two-echelon supply chain with an upstream supplier who operates under demand uncertainty and multiple downstream retailers who compete over quantity. The supplier's belief about retail…
We consider a stationary Markov process that models certain queues with a bulk service of a fixed number $m$ of admitted customers. We find an integral expression of its transition probability function in terms of certain multi-orthogonal…
In this work, we investigate information freshness in a status update communication system consisting of a source-destination link. Initially, we study the properties of a sample path of the age of information (AoI) process at the…
We analyze a tandem network of polling queues with two product types and two stations. We assume that external arrivals to the network follow a Poisson process, and service times at each station are exponentially distributed. For this…
In this paper we analyze the probability of consistency of sensor data distribution systems (SDDS), and determine suitable evaluation models. This problem is typically difficult, since a reliable model taking into account all parameters and…
We introduce a multiclass single-server queueing system in which the arrival rates depend on the current job in service. The system is characterized by a matrix of arrival rates in lieu of a vector of arrival rates. Our proposed model…
The supermarket model refers to a system with a large number of queues, where new customers choose d queues at random and join the one with the fewest customers. This model demonstrates the power of even small amounts of choice, as compared…
In this paper we consider a single-server, cyclic polling system with switch-over times. A distinguishing feature of the model is that the rates of the Poisson arrival processes at the various queues depend on the server location. For this…
As job redundancy has been recognized as an effective means to improve performance of large-scale computer systems, queueing systems with redundancy have been studied by various authors. Existing results include methods to compute the queue…
We study a many-server queuing system with general service time distribution and state dependent service rates. The dynamics of the system are modeled using measure valued processes which keep track of the residual service times. Under…
Stochastic processes find applications in modelling systems in a variety of disciplines. A large number of stochastic models considered are Markovian in nature. It is often observed that higher order Markov processes can model the data…
We consider a service system where agents (or, servers) are invited on-demand. Customers arrive as a Poisson process and join a customer queue. Customer service times are i.i.d. exponential. Agents' behavior is random in two respects.…
The problem of load balancing in a distribution network under unknown time- varying demand and supply is studied. A set of distributed controllers which regulate the amount of flow through the edges is designed to guarantee convergence of…
We investigate the stability condition of redundancy-$d$ multi-server systems. Each server has its own queue and implements popular scheduling disciplines such as First-Come-First-Serve (FCFS), Processor Sharing (PS), and Random Order of…
We consider Palm distributions arising in a Markov process with time homogeneous transitions which is jointly stationary with multiple point processes. Motivated by a BAR approach studied in the recent paper Braverman, Dai and Miyazawa…
We consider a general queueing system with price-sensitive customers in which the service provider seeks to balance two objectives, maximizing the average revenue rate and minimizing the average queue length. Customers arrive according to a…