Mahdi Ghamkhari

Optimal Charging of Electric Vehicles With Uncertain Departure Times: A Closed-Form Solution

In this paper, we show that an uncertain departure time significantly changes the analysis in optimizing the charging schedule of electric vehicles (EVs). We also obtain a closed-form solution for the stochastic optimization problem that is formulated to schedule charging of EVs with uncertain departure times in presence of hourly time-of-use pricing tariffs.

Optimal risk-aware power procurement for data centers in day-ahead and real-time electricity markets

With the growing trend in the amount of power consumed by data centers, finding ways to cut their electricity bills has become an important and challenging problem. In this paper, our focus is on the cost reduction that data centers may achieve by exploiting the diversity in the price of electricity in day-ahead and real-time electricity markets. Based on a stochastic optimization framework, we propose to jointly select a data centers service rate and its power demand bids to the day-ahead and real-time electricity markets. In our analysis, we take into account service-level-agreements, risk management constraints, and statistical characteristics of workload and electricity prices. Using empirical electricity price and Internet workload data and through computer simulations, we show that by directly participating in the day-ahead and real-time electricity markets, data centers can significantly reduce their energy expenditure.

Extending Demand Response to Tenants in Cloud Data Centers via Non-Intrusive Workload Flexibility Pricing

Participating in demand response programs is a promising tool for reducing energy costs in data centers by modulating energy consumption. Toward this end, data centers can employ a rich set of resource management knobs, such as workload shifting and dynamic server provisioning. Nonetheless, these knobs may not be readily available in a cloud data center (CDC) that serves cloud tenants/users, because workloads in CDCs are managed by tenants themselves who are typically charged based on a usage-based or flat-rate pricing and often have no incentive to cooperate with the CDC operator for demand response and cost saving. Toward breaking such “split incentive” hurdle, a few recent studies have tried market-based mechanisms, such as dynamic pricing, inside CDCs. However, such mechanisms often rely on complex designs that are hard to implement and difficult to cope with by tenants. To address this limitation, we propose a novel incentive mechanism that is not dynamic, i.e., it keeps pricing for cloud resources unchanged for a long period. While it charges tenants based on a usage-based pricing (UP) as used by today’s major cloud operators, it rewards tenants proportionally based on the time length that tenants set as deadlines for completing their workloads. This new mechanism is called UP with monetary reward (UPMR). We demonstrate the effectiveness of UPMR both analytically and empirically, showing: 1) UPMR can effectively reduce the CDC’s peak power consumption and energy cost without decreasing the CDC’s profit and 2) UPMR outperforms the state-of-the-art approaches that are used by today’s CDC operators to charge their tenants in terms of the profit gained by the CDC.

Energy Portfolio Optimization of Data Centers

Data centers have diverse options to procure electricity. However, the current literature on exploiting these options is very fractured. Specifically, it is still not clear how utilizing one energy option may affect selecting other energy options. To address this open problem, we propose a unified energy portfolio optimization framework that takes into consideration a broad range of energy choices for data centers. Despite the complexity and nonlinearity of the original models, the proposed analysis boils down to solving tractable linear mixed-integer stochastic programs. Using experimental electricity market and Internet workload data, various insightful numerical observations are reported. It is shown that the key to link different energy options with different short- and long-term profit characteristics is to conduct risk management at different time horizons. Also, there is a direct relationship between data centers’ service-level agreement parameters and their ability to exploit certain energy options. The use of on-site storage and the deployment of geographical workload distribution can particularly help data centers in utilizing high-risk energy choices, such as offering ancillary services or participating in wholesale electricity markets.

Strategic Bidding for Producers in Nodal Electricity Markets: A Convex Relaxation Approach

Strategic bidding problems in electricity markets are widely studied in power systems, often by formulating complex bi-level optimization problems that are hard to solve. The state-of-the-art approach to solve such problems is to reformulate them as mixed-integer linear programs (MILPs). However, the computational time of such MILP reformulations grows dramatically, once the network size increases, scheduling horizon increases, or randomness is taken into consideration. In this paper, we take a fundamentally different approach and propose effective and customized convex programming tools to solve the strategic bidding problem for producers in nodal electricity markets. Our approach is inspired by the Schmudgens Positivstellensatz Theorem in semialgebraic geometry; but then we go through several steps based upon both convex optimization and mixed-integer programming that results in obtaining close to optimal bidding solutions, as evidenced by several numerical case studies, besides having a huge advantage on reducing computation time. While the computation time of the state-of-the-art MILP approach grows exponentially when we increase the scheduling horizon or the number of random scenarios, the computation time of our approach increases rather linearly.

A Convex Optimization Framework for Service Rate Allocation in Finite Communications Buffers

We study the convexity of loss probability in communications and networking optimization problems that involve finite buffers, where the arrival process has a general distribution. Examples of such problems include scheduling, energy management and revenue, and cost optimization problems. To achieve a computationally tractable optimization framework, we propose to adjust an existing nonconvex loss probability formula for G/D/1 queues to present a convex and even more accurate loss probability model. We then use empirical data and computer simulations to examine the performance of the proposed design.