Jayakrishnan Nair

Energy procurement strategies in the presence of intermittent sources

The increasing penetration of intermittent, unpredictable renewable energy sources such as wind energy, poses significant challenges for utility companies trying to incorporate renewable energy in their portfolio. In this work, we study the problem of conventional energy procurement in the presence of intermittent renewable resources. We model the problem as a variant of the newsvendor problem, in which the presence of renewable resources induces supply side uncertainty, and in which conventional energy may be procured in three stages to balance supply and demand. We compute closed-form expressions for the optimal energy procurement strategy and study the impact of increasing renewable penetration, and of proposed changes to the structure of electricity markets. We explicitly characterize the impact of a growing renewable penetration on the procurement policy by considering a scaling regime that models the aggregation of unpredictable renewable sources. A key insight from our results is that there is a separation between the impact of the stochastic nature of this aggregation, and the impact of market structure and forecast accuracy. Additionally, we study the impact on procurement of two proposed changes to the market structure: the addition and the placement of an intermediate market. We show that addition of an intermediate market does not necessarily increase the efficiency of utilization of renewable sources. Further, we show that the optimal placement of the intermediate market is insensitive to the level of renewable penetration.

File Fragmentation over an Unreliable Channel

It has been recently discovered that heavy-tailed file completion time can result from protocol interaction even when file sizes are light-tailed. A key to this phenomenon is the RESTART feature where if a file transfer is interrupted before it is completed, the transfer needs to restart from the beginning. In this paper, we show that independent or bounded fragmentation produces light-tailed file completion time as long as the file size is light-tailed, i.e., in this case, heavy-tailed file completion time can only originate from heavy-tailed file sizes. If the file size is heavy-tailed, then the file completion time is clearly heavy-tailed. For this case, we show that when the file size distribution is regularly varying, then under independent or bounded fragmentation, the completion time tail distribution function is asymptotically upper bounded by that of the original file size stretched by a constant factor. We then prove that if the failure distribution has non-decreasing failure rate, the expected completion time is minimized by dividing the file into equal sized fragments; this optimal fragment size is unique but depends on the file size. We also present a simple blind fragmentation policy where the fragment sizes are constant and independent of the file size and prove that it is asymptotically optimal. Finally, we bound the error in expected completion time due to error in modeling of the failure process.

Provisioning of Large-Scale Systems: The Interplay Between Network Effects and Strategic Behavior in the User Base

In this paper, we consider the problem of capacity provisioning for an online service supported by advertising. We analyse the strategic interaction between the service provider and the user base in this setting, modeling positive network effects, as well as congestion sensitivity in the user base. We focus specifically on the influence of positive network effects, as well as the impact of noncooperative behavior in the user base on the firm’s capacity provisioning decision and its profit. Our analysis reveals that stronger positive network effects, as well as noncooperation in the user base, drive the service into a more congested state and lead to increased profit for the service provider. However, the impact of noncooperation, or “anarchy” in the user base strongly dominates the impact of network effects.

When heavy-tailed and light-tailed flows compete: The response time tail under generalized max-weight scheduling

This paper focuses on the design and analysis of scheduling policies for multi-class queues, such as those found in wireless networks and high-speed switches. In this context, we study the response-time tail under generalized max-weight policies in settings where the traffic flows are highly asymmetric. Specifically, we consider a setting where a bursty flow, modeled using heavy-tailed statistics, competes with a more benign, light-tailed flow. In this setting, we prove that classical max-weight scheduling, which is known to be throughput optimal, results in the light-tailed flow having heavy-tailed response times. However, we show that via a careful design of inter-queue scheduling policy (from the class of generalized max-weight policies) and intra-queue scheduling policies, it is possible to maintain throughput optimality, and guarantee light-tailed delays for the light-tailed flow, without affecting the response-time tail for the heavy-tailed flow.

Exploiting network effects in the provisioning of large scale systems

Online services today are characterized by a highly congestion sensitive user base, that also experiences strong positive network effects. A majority of these services are supported by advertising and are offered for free to the end user. We study the problem of optimal capacity provisioning for a profit maximizing firm operating such an online service in the asymptotic regime of a large market size. We show that network effects heavily influence the optimal capacity provisioning strategy, as well as the profit of the firm. In particular, strong positive network effects allow the firm to operate the service with fewer servers, which translates to increased profit.

When heavy-tailed and light-tailed flows compete: the response time tail under generalized max-weight scheduling

This paper focuses on the design and analysis of scheduling policies for multi-class queues, such as those found in wireless networks and high-speed switches. In this context, we study the response-time tail under generalized max-weight policies in settings where the traffic flows are highly asymmetric. Specifically, we consider a setting where a bursty flow, modeled using heavy-tailed statistics, competes with a more benign, light-tailed flow. In this setting, we prove that classical max-weight scheduling, which is known to be throughput optimal, results in the light-tailed flow having heavy-tailed response times. However, we show that via a careful design of inter-queue scheduling policy (from the class of generalized max-weight policies) and intra-queue scheduling policies, it is possible to maintain throughput optimality, and guarantee light-tailed delays for the light-tailed flow, without affecting the response-time tail for the heavy-tailed flow.

Opportunistic adaptive haptic sampling on forward channel in telehaptic communication

We propose a network-based opportunistic improvisation to adaptive sampling for the forward channel telehaptic data stream on a time-varying network. The algorithm explores real-time tuning of the perceptual deadband parameter to minimize network underutilization, and consequently improves the quality of telehaptic communication. We describe in detail the rationale behind the design choices of the proposed sampling scheme. We perform both real-time telehaptic experiments and simulations to test the proof of concept. The reconstructed haptic signals reveal a substantial improvement in average SNR of 3.57 dB, suggesting that the proposed method outperforms the conventional adaptive sampling technique to a large extent. In addition to satisfying the telehaptic Quality of Service (QoS) requirements, we also demonstrate that our method does not overwhelm the network or penalize the concurrent traffic streams.

Optimal job fragmentation

It has been recently discovered that on an unreliable server, the job completion time distribution function (df) can be heavy-tailed (HT) even when job size df is light-tailed (LT) [1, 5]. A key to this phenomenon is the RESTART feature where if a job is interrupted in the middle of its processing, the entire job needs to restart from the beginning, i.e., the work that is partially completed is lost. A standard mechanism for reducing the job completion time in an unreliable service environment is checkpointing [3, 4, 6]. We view checkpointing as a job fragmentation operation, where the server processes one fragment of the job at a time. If the server becomes unavailable, say due to failure, then only the work corresponding to the fragment being processed at the time of failure is lost. In this paper, we are motivated by the question: Can fragmentation ‘lighten’ the tail df of the completion time? In Section 3, we provide sufficient conditions on the fragmentation policy that gives rise to LT completion time so long as the job size df is LT. We then characterize the optimal fragmentation policy seeking to minimize the expected job completion time. This policy requires a priori knowledge of the job size. We then describe a sub-optimal fragmentation policy that is blind to the job size and is provably very close to optimal. We also describe the asymptotic tail behavior of the job completion time df under both policies. Assuming the server unavailability periods are LT, both policies produce LT completion times when the job size df is LT. For the case of regularly varying job size df, the job completion time under both policies is regularly varying with the same degree - this is the lightest possible asymptotic tail behavior (in the degree sense).

On the probability of current and temperature overloading in power grids: a large deviations approach

The advent of renewable energy sources has huge implications for the design and control of power grids. On the engineering side, reliability is currently ensured by strict con- straints on current, voltage and temperature. However, with growing supply-side uncertainty induced by renewables, these will need to be replaced by probabilistic guarantees, allowing constraints on a given line to be violated with a low probability, e.g., several minutes per year. In the present note we illustrate, using large deviations techniques, how replacing (probabilistic) current constraints by temperature constraints can lead to capacity gains in power grids.

On competitive provisioning of ad-supported cloud services

Motivated by cloud services with ad-supported revenues, we consider the interplay of network effects, congestion, and competition in determining the market structure in such environments. In particular, we study the strategic interactions between competing service providers and a user base, modeling congestion sensitivity and two forms of positive network effects: “firm-specific” versus “industry-wide.” Our analysis reveals that users are generally no better off due to competition in a marketplace of ad-supported services as the congestion levels are of the same order as if there were only one firm. Further, our analysis highlights an important contrast between firm-specific and industry-wide network effects: multiple firms can coexist in a marketplace with industry-wide network effects, but near-monopolies tend to emerge in marketplaces with firm-specific network effects.