We model the aggregate overnight demand for electricity by a large community of (possibly hybrid) plug-in electric vehicles (PEVs) each of whose power demand follows a prescribed profile and is interruptible. The community is served by a regional electrical utility which is assumed to purchase electricity from a state/national distribution grid according to a flat-rate Φ per kilowatt-unit-time up to a threshold L, and thereafter overage (demand >; L) charges π >; Φ are leveed per kilowatt-unit-time. Rather than a spot-price system for household consumers (which would necessarily need to be operated by automated means overnight when most consumers sleep), the “grid” (regional utility) is “smart” in that it monitors its total load and, when overages threaten, can reduce load by signaling certain consumers to interrupt charging and defer their charging load by one unit of time. In this paper, we model the uninterrupted load by a Gaussian process which we justify by means of a functional central limit theorem (FCLT). This limiting Gaussian process is the arrival process of a discrete-time queue which is used to model the (partially) interrupted and deferred load over a finite time-horizon. We can then compute the mean amount of overage at the end of this time horizon (say at 6 AM when charging is to be completed ahead of the morning commute).

Takis Konstantopoulos; Response to Prof. Baccelli's lecture on Modelling of Wireless Communication Networks by Stochastic Geometry, The Computer Journal, Volume

We propose a new model for file-sharing peer-to-peer (P2P) networks that mimics the incentives provided by the popular BitTorrent system. In it, larger files are split into chunks and a peer can download or swap only one chunk at a time. We propose a Markov chain model in continuous time that resembles a stochastic epidemic/coagulation model. We prove that the Markov chain is approximated by a differential equation which, by itself, can give some rough information about the performance of the system. Finally, using this model, we explore the performance of BitTorrent-like incentives for an open system with peer departures and arrivals and a single file (torrent) with two chunks.

We consider bursty data communications in code-division multiple-access (CDMA) cellular networks. The significant fluctuation of the cochannel multiple-access interference (MAI) in such systems makes it very challenging to carry out radio resource management. A main goal of this paper is to obtain a fundamental understanding of the temporal correlation structure of the MAI, which plays a crucial role in effective resource allocation. To this end, we take a cross-layer design approach, and characterize the stochastic MAI process while taking into account both the burstiness of data traffic and time-varying channel conditions. Our main results reveal that under standard assumptions on ON/OFF traffic flows and fading channels, the MAI process exhibits scale-invariant burstiness and is "self-similar" (with Hurst parameter 1/2<H<1), in both the uplink and the downlink cases. The MAI self-similarity indicates that the MAI levels are long-range dependent and therefore there exists a nontrivial predictive MAI structure across multiple time scales. The predictive MAI structure can be utilized for effective interference management through dynamic resource allocation. We illustrate this via a rate control scheme based on the MAI prediction, and our results show that the performance gain is substantial. The exploitation of the MAI temporal correlation structure for resource allocation parallels and complements multiuser detection which utilizes the MAI snapshot structure at the symbol level.

We consider the stability and performance of a model for networks supporting services that adapt their transmission to the available bandwidth. Not unlike real networks, in our model, connection arrivals are stochastic, each has a random amount of data to send, and the number of ongoing connections in the system changes over time. Consequently, the bandwidth allocated to, or throughput achieved by, a given connection may change during its lifetime as feedback control mechanisms react to network loads. Ideally, if there were a fixed number of ongoing connections, such feedback mechanisms would reach an equilibrium bandwidth allocation typically characterized in terms of its "fairness" to users, e.g., max-min or proportionally fair. We prove the stability of such networks when the offered load on each link does not exceed its capacity. We use simulation to investigate performance, in terms of average connection delays, for various fairness criteria. Finally, we pose an architectural problem in TCP/IPs decoupling of the transport and network layer from the point of view of guaranteeing connection-level stability, which we claim may explain congestion phenomena on the Internet.

We consider a variable bit-rate connection with a deterministically shaped random traffic process, as specified by communications networking standards. Regarding randomness, we assume no restricted model other than the natural requirement that the process be stationary and ergodic. Given only the shape parameters, we consider the open problem of determining the maximum service bandwidth required to achieve a given bound on the probability that the packet-transfer delay exceeds a certain threshold. The shape parameters together with a probabilistic bound on the packet-transfer delay define a variable bit-rate "channel"; an equivalent problem is to determine the "capacity" of this channel. To this end, we consider a queue with a constant service rate and a shaped arrival process and obtain tight bounds on queue occupancy and queueing delay. In particular, we describe that traffic pattern (among all stationary-ergodic and deterministically constrained arrival processes) which achieves the probabilistic bound.

We investigate the problem of virtual path (VP) capacity allocation in a decentralized way. Users (VP controllers), sharing common network resources, are assumed to control their VP capacities according to their performance measures. We formulate a model that differs from previous ones in two points: first, each user has its own performance objective that is simply assumed to be concave and smooth; second, a user's strategy (VP bandwidth reservation) is constrained between two numbers. Adopting a standard game-theoretic formulation, we prove that there exists a unique network operating point-Nash equilibrium. We show several interesting properties of the equilibrium and also look at the convergence of some distributed algorithms. After studying the combined problem of routing and flow control in parallel link networks, we investigate the problem of VP capacity allocation in general topology networks, where fixed routing is assumed. Finally, examples of the model are presented.

We consider the stability and performance of a model for networks supporting services that adapt their transmission to the available bandwidth. Not unlike real networks, in our model connection arrivals are stochastic and have a random amount of data to send, so the number of connections in the system changes over time. In turn the bandwidth allocated to, or throughput achieved by, a given connection, may change during its lifetime due to feedback control mechanisms that react to congestion and thus implicitly to the number of ongoing connections. Ideally, for a fixed number of connections, such mechanisms reach an equilibrium typically characterized in terms of its 'fairness' in allocating bandwidth to users, e.g., max-min fair. We prove the stability of such networks when the offered load on each link does not exceed its capacity. We use simulation to investigate the performance, in terms of average connection delays, for various network topologies and fairness criteria. Finally we pose an architectural problem in TCP/IP's decoupling of the transport and network layer from the point of view of guaranteeing connection level stability, which we claim may explain congestion phenomena on the Internet.

The problem of designing burst reducing flow controllers for traffic in an ATM network is studied. By requiring that the output flow obey certain burstiness constraints, it is shown that an optimal design exists and that it can be easily implemented in real time. Two versions of the problem are considered. The first one places constraints on the buffer size and the second one on the maximum delay that a cell can experience. Both problems are solved for arbitrary traffic processes. To treat the problems in this generality the authors introduce reflection mappings and use them, in a rather novel way, to establish optimality results. As a by-product of the analysis and methods, the optimality of the popular leaky bucket flow control scheme is also established.>

The leaky bucket is a simple flow control scheme for ATM networks. An arriving cell can be transmitted only if it finds a token in the token buffer, in which case it is transmitted instantaneously by consuming a token. If the token buffer is empty, the cell has to wait until the generation of a new token. For purposes of analysis the authors assume an infinite cell buffer. The control parameter is the token buffer size C. The authors examine the burstiness of the output how as a function of C and show that the burstiness increases with C. In particular the output flow is always less bursty than the input flow. This monotonicity simplifies optimal choice of the token buffer size. The result is true for fairly arbitrary input flows and deterministic token generation times.>