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In their early days, Twitter, Flickr, Etsy, and many other companies experienced sudden spikes in activity that took their web services down in minutes. Today, determining how much capacity you need for handling traffic surges is still a common frustration of operations engineers and software developers. This hands-on guide provides the knowledge and tools you need to measure, deploy, and manage your web application infrastructure before you experience explosive growth.

Capacity is the maximum short-run output with capital in place under normal operations, and capital investment increases capacity. Excess capacity can be used as entry deterrence by lowering average costs over a greater range of output, and as an operations strategy by providing value through flexibility to manage demand fluctuations and production disturbances. We study the way that information technology (IT) can contribute to a strategy of holding excess capacity by comparing the relationship between IT capital and capacity with that of non-IT capital and capacity. We find that increases in IT capital yield almost fourfold greater expansion in capacity than do increases in non-IT capital. Thus, as both types of capital are constraints on capacity, for a strategy of holding excess capacity, IT capital is a more valuable constraint to relax than non-IT capital. In addition, since the late 1990s, IT capital and, to a lesser extent, non-IT capital have reduced capacity utilization (output divided by capacity), meaning increasing levels of excess capacity are being held across manufacturing industries and utilities across the economy. Capacity is the maximum short-run output with capital in place under normal operations, and capital investment increases capacity. Excess capacity can be used as an economic strategy for entry deterrence by lowering average costs over a greater range of output, and as an operations strategy by providing value through flexibility to manage demand fluctuations and production disturbances. Our primary focus is to study the way that information technology (IT) can contribute to a strategy of holding excess capacity by comparing the relationship between IT capital and capacity with that of non-IT capital and capacity. Using production theory–based empirical analyses, we find that increases in IT capital yield almost fourfold greater expansion in capacity than do increases in non-IT capital. Thus, as both types of capital are constraints on capacity, for a strategy of holding excess capacity IT capital is a more valuable constraint to relax than non-IT capital. In addition, since the late 1990s, IT capital, and to a lesser extent, non-IT capital, has reduced capacity utilization (output/capacity), meaning increasing levels of excess capacity are being held across manufacturing industries and utilities across the economy.

Background Capacity strengthening initiatives aimed at increasing research knowledge and skills of investigators in low- and middle-income countries (LMICs) have been implemented over the last several decades. With increased capacity, local investigators will have greater leadership in defining research priorities and impact policy change to help improve health outcomes. Evaluations of models of capacity strengthening programs are often limited to short-term impact. Noting the limitations of traditional output-based evaluations, we utilized a broader framework to evaluate the long-term impact of the Vanderbilt Institute in Research Development and Ethics (VIRDE), a decade-old intensive grant development practicum specifically tailored for investigators from LMICs. Methods To assess the impact of VIRDE on the research careers of alumni over the past 10 years, we surveyed alumni on research engagement, grant productivity, career trajectory, and knowledge gained in grant writing. Descriptive statistics, including means and total counts, and paired sample t-tests were used to analyze the data. Results Forty-six of 58 alumni completed the survey. All respondents returned to their home countries and are currently engaged in research. Post-VIRDE grant writing knowledge ratings were significantly greater than pre-VIRDE. The number of respondents submitting grants post-VIRDE was 2.6 times higher than before the program. Eighty-three percent of respondents submitted a total of 147 grants post-VIRDE, of which 45.6% were awarded. Respondents acknowledged VIRDE’s positive impact on career growth and leadership, with 88% advancing in career stage. Conclusions Gains in grant writing knowledge and grant productivity suggest that VIRDE scholars built skills and confidence in grant writing during the program. A substantial proportion of respondents have advanced in their careers and continue to work in academia in their country of origin. Results show a sustained impact on the research careers of VIRDE alumni. The broader framework for research capacity strengthening resulted in an expansive assessment of the VIRDE program and alumni, illuminating successful program elements and implications that can inform similar capacity strengthening programs.

We study a capacity sizing problem in a service system that is modeled as a single-class queue with multiple servers and where customers may renege while waiting for service. A salient feature of the model is that the mean arrival rate of work is random (in practice this is a typical consequence of forecasting errors). The paper elucidates the impact of uncertainty on the nature of capacity prescriptions, and relates these to well established rules-of-thumb such as the square-root safety staffing principle. We establish a simple and intuitive relationship between the incoming load (measured in Erlangs) and the extent of uncertainty in arrival rates (measured via the coefficient of variation) that characterizes the extent to which uncertainty dominates stochastic variability or vice versa. In the former case it is shown that traditional square-root safety staffing logic is no longer valid, yet simple capacity prescriptions derived via a suitable newsvendor problem are surprisingly accurate.

Background We propose a mathematical model formulated as a finite-horizon Markov Decision Process (MDP) to allocate capacity in a radiology department that serves different types of patients. To the best of our knowledge, this is the first attempt at considering radiology resources with different capacities and individual no-show probabilities of ambulatory patients in an MDP model. To mitigate the negative impacts of no-show, overbooking rules are also investigated. Methods The model’s main objective is to identify an optimal policy for allocating the available capacity such that waiting, overtime, and penalty costs are minimized. Optimization is carried out using traditional dynamic programming (DP). The model was applied to real data from a radiology department of a large Brazilian public hospital. The optimal policy is compared with five alternative policies, one of which resembles the one currently used by the department. We identify among alternative policies the one that performs closest to the optimal. Results The optimal policy presented the best performance (smallest total daily cost) in the majority of analyzed scenarios (212 out of 216). Numerical analyses allowed us to recommend the use of the optimal policy for capacity allocation with a double overbooking rule and two resources available in overtime periods. An alternative policy in which outpatients are prioritized for service (rather than inpatients) displayed results closest to the optimal policy, being also recommended due to its easy implementation. Conclusions Based on such recommendation and observing the state of the system at any given period (representing the number of patients waiting for service), radiology department managers should be able to make a decision (i.e., define number and type of patients) that should be selected for service such that the system’s cost is minimized.

We consider the problem faced by an airline that is flying both passengers and cargo over a network of locations on a fixed periodic schedule. Bookings for many classes of cargo shipments between origin-destination pairs in this network are made in advance, but the weight and volume of aircraft capacity available for cargo as well as the exact weight and volume of each shipment are not known at the time of booking. The problem is to control cargo accept/reject decisions to maximize expected profits while ensuring effective dispatch of accepted shipments through the network. This network stochastic dynamic control problem has very high computational complexity. We propose a linear programming and stochastic simulation-based computational method for learning approximate control policies and discuss their structural properties. The proposed method is flexible and can utilize historical booking data as well as decisions generated by default control policies.

We consider the allocation of capacity in a system in which rental equipment is accessed by two classes of customers. We formulate the problem as a continuous-time analogue of the one-shot allocation problems found in the more traditional literature on revenue management, and we analyze a queueing control model that approximates its dynamics. Our investigation yields three sets of results. First, we use dynamic programming to characterize properties of optimal capacity allocation policies. We identify conditions under which \"complete sharing\"—in which both classes of customers have unlimited access to the rental fleet—is optimal. Next, we develop a computationally efficient \"aggregate threshold\" heuristic that is based on a fluid approximation of the original stochastic model. We obtain closed-form expressions for the heuristic’s control parameters and show that the heuristic performs well in numerical experiments. The closed-form expressions also show that, in the context of the fluid approximation, revenues are concave and increasing in the fleet size. Finally, we consider the effect of the ability to allocate capacity on optimal fleet size. We show that the optimal fleet size under allocation policies may be lower, the same as, or higher than that under complete sharing. As capacity costs increase, allocation policies allow for larger relative fleet sizes. Numerical results show that, even in cases in which dollar profits under complete sharing may be close to those under allocation policies, the capacity reductions enabled by allocation schemes can help to lift profit margins significantly.

We study a capacity sizing problem in a service system that is modeled as a single-class queue with multiple servers and where customers may renege while waiting for service. A salient feature of the model is that the mean arrival rate of work is random (in practice this is a typical consequence of forecasting errors). The paper elucidates the impact of uncertainty on the nature of capacity prescriptions, and relates these to well established rules-of-thumb such as the square-root safety staffing principle. We establish a simple and intuitive relationship between the incoming load (measured in Erlangs) and the extent of uncertainty in arrival rates (measured via the coefficient of variation) that characterizes the extent to which uncertainty dominates stochastic variability or vice versa. In the former case it is shown that traditional square-root safety staffing logic is no longer valid, yet simple capacity prescriptions derived via a suitable newsvendor problem are surprisingly accurate.

Merger and acquisition activity has increased sharply in the last decade. It seems useful to have models that can help senior managers of bidder firms make informed decisions about the amount of premium, over the target's share prices prevailing prior to merger announcement, that can be justified on the basis of operational synergies . The goal of this article is to capture important parameters from the production side that have a bearing on the valuation of the target's shares. We show that the production characteristics of both the bidder and the target matter in a significant way. For example, if the bidder and target operate in independent markets, the bidder has flexible production facilities but the target's production facilities are inflexible, then an increase in the bidder's demand can make the target less attractive and lower the value of operational synergy.

The declining cost of information technology (IT) over time provides the later entrant in information-intensive industries a cost advantage. On the other hand, the earlier entrant has the potential to build and retain its market share if consumers incur a cost in switching to the later entrant. We investigate the impact of a decline in the IT cost and the switching cost on IT investment strategies of firms. We find that a declining IT cost always hurts the early entrant's profit. The early entrant may assume an aggressive investment strategy or a defensive investment strategy in response to a decline in the IT cost, depending on whether the switching cost relative to the extent of decline in the IT cost is high or low, respectively. A decline in IT cost also hurts the later entrant's profit if the switching cost is high. A surprising result is that when the decline in the IT cost is higher than a critical value, a higher switching cost increases consumer surplus. When firms control the switching cost, the early entrant increases its investment in quality and switching cost and maintains its quality and its market-share leadership irrespective of the extent of decline in the IT cost.