Related papers: On a loss storage network with finite capacity
We study the robustness of flow networks against cascading failures under a partial load redistribution model. In particular, we consider a flow network of $N$ lines with initial loads $L_1, \ldots, L_N$ and free-spaces (i.e., redundant…
This work considers a many-server queueing system in which customers with i.i.d., generally distributed service times enter service in the order of arrival. The dynamics of the system is represented in terms of a process that describes the…
We study deterministic continuous-time lossy dynamical flow networks with constant exogenous demands, fixed routing, and finite flow and buffer capacities. In the considered model, when the total net flow in a cell ---consisting of the…
This work investigates the effect of finite buffer sizes on the throughput capacity and packet delay of line networks with packet erasure links that have perfect feedback. These performance measures are shown to be linked to the stationary…
We review selected results related to robustness of networked systems in finite and asymptotically large size regimes, under static and dynamical settings. In the static setting, within the framework of flow over finite networks, we discuss…
This work considers a server that processes $J$ classes using the generalized processor sharing discipline with base weight vector $\alpha=(\alpha _1,...,\alpha_J)$ and redistribution weight vector $\beta=(\beta_1,...,\beta_J)$. The…
One of the primary objectives of a distributed storage system is to reliably store large amounts of source data for long durations using a large number $N$ of unreliable storage nodes, each with $c$ bits of storage capacity. Storage nodes…
Time-dependent models of fluid motion in thin layers, subject to signed source terms, represent important sub-problems within climate dynamics. Examples include ice sheets, sea ice, and even shallow oceans and lakes. We address these…
In this work we are interested in dealing with single-phase flows in fractured porous media for underground processes. We focus our attention on domains where the presence of faults, with thickness several orders of magnitude smaller than…
The explosion in the volumes of data being stored online has resulted in distributed storage systems transitioning to erasure coding based schemes. Yet, the codes being deployed in practice are fairly short. In this work, we address what we…
Streaming is a model where an input graph is provided one edge at a time, instead of being able to inspect it at will. In this work, we take a parameterized approach by assuming a vertex cover of the graph is given, building on work of…
We consider a model of Internet congestion control that represents the randomly varying number of flows present in a network where bandwidth is shared fairly between document transfers. We study critical fluid models obtained as formal…
The motivation for this work stems from the problem of scheduling requests for flow at supply points along an automated network of open-water channels. The off-take flows are rigid-profile inputs to the system dynamics. In particular, the…
Robustness of routing policies for networks is a central problem which is gaining increased attention with a growing awareness to safeguard critical infrastructure networks against natural and man-induced disruptions. Routing under limited…
In this paper, we generalize the minimum flow decomposition problem (MFD) to incorporate uncertain edge capacities and tackle it from the perspective of robust optimization. In the classical flow decomposition problem, a network flow is…
We consider the setting of distributed storage system where a single file is subdivided into smaller fragments of same size which are then replicated with a common replication factor across servers of identical cache size. An incoming file…
Incompressibility is a fundamental condition in most fluid models. Accumulation of simulation errors violates it and causes volume loss. Past work suggested correction methods to battle it. These methods, however, are imperfect and in some…
Drone delivery systems violate a core assumption in classical queueing models: server capacity is not fixed. Drones (servers) periodically must recharge, creating random fluctuations in service availability. We introduce an Erlang--S$^{*}$…
Edge systems promise to bring data and computing closer to the users of time-critical applications. Specifically, edge storage systems are emerging as a new system paradigm, where users can retrieve data from small-scale servers…
We introduce a dynamical model of node repair in distributed storage systems wherein the storage nodes are subjected to failures according to independent Poisson processes. The main parameter that we study is the time-average capacity of…