Related papers: Extreme Values in Closed Networks
A class of queueing networks which may have an arbitrary topology, and consist of single-server fork-join nodes with both infinite and finite buffers is examined to derive a representation of the network dynamics in terms of max-plus…
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…
A multi-class single-server queueing model with finite buffers, in which scheduling and admission of customers are subject to control, is studied in the moderate deviation heavy traffic regime. A risk-sensitive cost set over a finite time…
In this paper we analyze a single server queue with batch arrivals and semi-Markovian service times. We also include the feature that the first service of each busy period might have a different distribution than subsequent service times.…
Considering a Manhattan mobility model in vehicle-to-vehicle networks, this work studies a power minimization problem subject to second-order statistical constraints on latency and reliability, captured by a network-wide maximal data queue…
We consider a multi-server queue in the Halfin-Whitt regime: as the number of servers $n$ grows without a bound, the utilization approaches 1 from below at the rate $\Theta(1/\sqrt{n})$. Assuming that the service time distribution is…
In this work, a growing network model that can generate a random network with finite degree in infinite time is studied. The dynamics are governed by a rule where the degree increases under a scheme similar to the Malthus-Verhulst model in…
Motivated by the Quality-of-Service (QoS) buffer management problem, we consider online scheduling of packets with hard deadlines in a finite capacity queue. At any time, a queue can store at most $b \in \mathbb Z^+$ packets. Packets arrive…
In this paper, we consider the occupancy distribution for an open network of infinite server queues with multivariate batch arrivals following a non-homogeneous Poisson process, and general service time distributions. We derive a…
This paper introduces a novel approach employing extreme value theory to analyze queue lengths within a corridor controlled by adaptive controllers. We consider the maximum queue lengths of a signalized corridor consisting of nine…
We consider a switched (queuing) network in which there are constraints on which queues may be served simultaneously; such networks have been used to effectively model input-queued switches and wireless networks. The scheduling policy for…
This work presents exact expressions for size distributions of weak/multilayer connected components in two generalisations of the configuration model: networks with directed edges and multiplex networks with arbitrary number of layers. The…
We describe the structure of connected graphs with the minimum and maximum average distance, radius, diameter, betweenness centrality, efficiency and resistance distance, given their order and size. We find tight bounds on these graph…
We derive representation theorems for exchangeable distributions on finite and infinite graphs using elementary arguments based on geometric and graph-theoretic concepts. Our results elucidate some of the key differences, and their…
In traditional priority queues, we assume that every customer upon arrival has a fixed, class-dependent priority, and that a customer may not commence service if a customer with a higher priority is present in the queue. However, in…
The synchronization process inherent to the Bitcoin network gives rise to an infinite-server model with the unusual feature that customers interact. Among the closed-form characteristics that we derive for this model is the busy period…
A class of queueing networks which consist of single-server fork-join nodes with infinite buffers is examined to derive a representation of the network dynamics in terms of max-plus algebra. For the networks, we present a common dynamic…
We study extremal statistics and return intervals in stationary long-range correlated sequences for which the underlying probability density function is bounded and uniform. The extremal statistics we consider e.g., maximum relative to…
This note describes several open questions concerning scaling limits of queue-length processes of symmetric queues in heavy traffic, distinguishing between service-time distributions with finite and infinite variance.
We explore the dependence structure in the sampled sequence of large networks. We consider randomized algorithms to sample the nodes and study extremal properties in any associated stationary sequence of characteristics of interest like…