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Optimal PowerDown Strategies
"... We consider the problem of selecting threshold times to transition a device to lowpower sleep states during an idle period. The twostate case in which there is a single active and a single sleep state is a continuous version of the skirental problem. We consider a generalized version in which the ..."
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We consider the problem of selecting threshold times to transition a device to lowpower sleep states during an idle period. The twostate case in which there is a single active and a single sleep state is a continuous version of the skirental problem. We consider a generalized version in which there is more than one sleep state, each with its own power consumption rate and transition costs. We give an algorithm that, given a system, produces a deterministic strategy whose competitive ratio is arbitrarily close to optimal. We also give an algorithm to produce the optimal online strategy given a system and a probability distribution that generates the length of the idle period. We also give a simple algorithm that achieves a competitive ratio of 3 + 2 √ 2 ≈ 5.828 for any system.
RENT, LEASE OR BUY: RANDOMIZED ALGORITHMS FOR MULTISLOPE SKI RENTAL
"... Abstract. In the Multislope Ski Rental problem, the user needs a certain resource for some unknown period of time. To use the resource, the user must subscribe to one of several options, each of which consists of a onetime setup cost (“buying price”), and cost proportional to the duration of the us ..."
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Abstract. In the Multislope Ski Rental problem, the user needs a certain resource for some unknown period of time. To use the resource, the user must subscribe to one of several options, each of which consists of a onetime setup cost (“buying price”), and cost proportional to the duration of the usage (“rental rate”). The larger the price, the smaller the rent. The actual usage time is determined by an adversary, and the goal of an algorithm is to minimize the cost by choosing the best option at any point in time. Multislope Ski Rental is a natural generalization of the classical Ski Rental problem (where the only options are pure rent and pure buy), which is one of the fundamental problems of online computation. The Multislope Ski Rental problem is an abstraction of many problems where online decisions cannot be modeled by just two options, e.g., power management in systems which can be shut down in parts. In this paper we study randomized algorithms for Multislope Ski Rental. Our results include the best possible online randomized strategy for any additive instance, where the cost of switching from one option to another is the difference in their buying prices; and an algorithm that produces an ecompetitive randomized strategy for any (nonadditive) instance. 1.
On the Remote Server Problem or More about TCP Acknowledgments
"... We study an online problem that is motivated by service calls management in a remote support center. When a customer calls the remote support center of a software company, a Technician opens a service request and assigns it a severity rating. This request is then transferred to the appropriate Sup ..."
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We study an online problem that is motivated by service calls management in a remote support center. When a customer calls the remote support center of a software company, a Technician opens a service request and assigns it a severity rating. This request is then transferred to the appropriate Support Engineer (SE) who establishes a connection to the customer’s site and uses remote diagnostic capabilities to resolve the problem. We assume that the SE can service at most one customer at time and a request service time is negligible. There is a constant setup cost of creating a new connection to a customer’s site and a specific cost per request for delaying its service that depends on the severity of the request. The problem is to decide which customers to serve first so as to minimize the incurred cost. This problem with just two customers is a natural generalization of the TCP acknowledgment problem. For the online version of the Remote Server Problem (RSP), we present algorithms for the general case and for a special case of two customers that achieve competitive ratios of exactly 4 and 3, respectively. We also show that no deterministic online algorithm can have competitive ratio better that 3. Then we study generalized versions of our model, these are the case of an asymmetric setup cost function and the case of multiple SE’s. For the offline version of the RSP, we derive an optimal algorithm with a polynomial running time for a constant number of customers.
On the Best Possible Competitive Ratio for Multislope Ski Rental 1
"... Abstract The multislope skirental problem ..."
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Month 200X, Vol.21, No.X, pp.XX–XX J. Comput. Sci. & Technol. Competitive Analysis of Two Special Online Device Replacement Problems
"... Abstract When a new investment opportunity of purchasing a new device occurs, the investors must decide whether or not and when to buy this device in an online fashion. That is, the online player must make investment decision while neither future demand for the product nor future investment opportun ..."
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Abstract When a new investment opportunity of purchasing a new device occurs, the investors must decide whether or not and when to buy this device in an online fashion. That is, the online player must make investment decision while neither future demand for the product nor future investment opportunities are known. This problem which generalizes the basic leasing problem has been introduced by Azar et al., and then two special cases have been studied by Damaschke. In the socalled equal prices model a 2competitive algorithms is devised and a 1.618 lower bound is given. Here we make use of an averaging technique and obtain a better tight lower bound of 2, in other words, this lower bound can not be improved. Furthermore, another special case which only considers twostage device replacement is studied in this paper. Accounting for the interest rate is an essential feature of any reasonable financial model. Therefore, we explore the twostage model with and without the interest rate respectively. In addition, we introduce the riskreward model to analyze this problem and improve the competitive ratio performance.
Competitive analysis
"... On the online rentorbuy problem in probabilistic environments ..."
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