Related papers: On many-server queues in heavy traffic
In asymptotic regimes, both in time and space (network size), the derivation of network capacity results is grossly simplified by brushing aside queueing behavior in non-Jackson networks. This simplifying double-limit model, however, lends…
This paper establishes limit theorems for a class of stochastic hybrid systems (continuous deterministic dynamic coupled with jump Markov processes) in the fluid limit (small jumps at high frequency), thus extending known results for jump…
This paper considers a population process on a dynamically evolving graph, which can be alternatively interpreted as a queueing network. The queues are of infinite-server type, entailing that at each node all customers present are served in…
We consider large fluctuations, namely overload of servers, in a network with dynamic routing of messages. The servers form a circle. The number of input flows is equal to the number of servers, the messages of any flow are distributed…
We consider a connection-level model proposed by Massouli\'{e} and Roberts for bandwidth sharing among file transfer flows in a communication network. We study weighted proportionally fair sharing policies and establish explicit-form bounds…
We investigate, under general stationary ergodic assumptions, the stability of systems of $S$ parallel queues in which any incoming customer joins the queue of the server having the $p+1$-th shortest workload ($p < S$), or a free server if…
We consider a system of N queues with decentralized load balancing such as power-of-D strategies(where D may depend on N) and generic scheduling disciplines. To measure the dependence of the queues, we use the clan of ancestors, a technique…
We consider the FCFS $GI/GI/n$ queue, and prove the first simple and explicit bounds that scale as $\frac{1}{1-\rho}$ under only the assumption that inter-arrival times have finite second moment, and service times have finite $2+\epsilon$…
The model is motivated by the problem of load distribution in large-scale cloud-based data processing systems. We consider a heterogeneous service system, consisting of multiple large server pools. The pools are different in that their…
We study a single server queue operating under the shortest remaining processing time (SRPT) scheduling policy; that is, the server preemptively serves the job with the shortest remaining processing time first. In this work we are…
Multiserver queueing systems are found at the core of a wide variety of practical systems. Many important multiserver models have a previously-unexplained similarity: identical mean response time behavior is empirically observed in the…
In the context of fog computing, we consider a simple case when data centers are installed at the edge of the network and assume that if a request arrives at an overloaded data center, then it is forwarded to a neighboring data center with…
A service system with multiple types of customers, arriving as Poisson processes, is considered. The system has infinite number of servers, ranked by $1,2,3, \ldots$; a server rank is its ``location." Each customer has an independent…
Proportional fairness is a popular service allocation mechanism to describe and analyze the performance of data networks at flow level. Recently, several authors have shown that the invariant distribution of such networks admits a product…
Nonlinear time series models with exogenous regressors are essential in econometrics, queuing theory, and machine learning, though their statistical analysis remains incomplete. Key results, such as the law of large numbers and the…
We study a double-ended queue where buyers and sellers arrive to conduct trades. When there is a pair of buyer and seller in the system, they immediately transact a trade and leave. Thus there cannot be non-zero number of buyers and sellers…
We analyze the behavior of closed product-form queueing networks when the number of customers grows to infinity and remains proportionate on each route (or class). First, we focus on the stationary behavior and prove the conjecture that the…
We define a stochastic model of a two-sided limit order book in terms of its key quantities \textit{best bid [ask] price} and the \textit{standing buy [sell] volume density}. For a simple scaling of the discreteness parameters, that keeps…
We study a minimal model of traffic flows in complex networks, simple enough to get analytical results, but with a very rich phenomenology, presenting continuous, discontinuous as well as hybrid phase transitions between a free-flow phase…
Recently a functional limit theorem for sums of moving averages with random coefficients and i.i.d. heavy tailed innovations has been obtained under the assumption that all partial sums of the series of coefficients are a.s. bounded between…