A Queueing Model for Yield Management of Computing Centers Parijat Dube IBM Research, NY, USA Yezekael Hayel IRISA, Rennes, France INFORMS Annual Meeting, San Francisco, Nov , 2005

On Demand computing services On Demand means offering IT resources to firms when they need it, in the quantity that is required On Demand is a business model – it can be viewed as an alternative to the buy-and-service and lease models for IT hardware. It is also an alternative to purchasing software licenses for use on proprietary hardware. It means paying for use only, of IT hardware, software and networking resources.

On Demand computing services On Demand takes advantage of network speed and sophisticated “middleware”, which allows seamless operation of IT resources, remotely. On Demand is a win-win proposition, for the provider of the service and for the customer: The provider can experience considerable scale economies through resource sharing; The customer saves on outlay expenses, converts purchases to operating costs, and reaps the savings of the scale economies passed on by the provider.

Features of On Demand Temporary (very short term) increases and decreases in resource needs can be satisfied instantaneously, Temporary (very short term) increases and decreases in resource needs can be satisfied instantaneously, Neither space nor human resources need be consumed, or reassigned when no longer needed, Neither space nor human resources need be consumed, or reassigned when no longer needed, There is opportunity to pool resources. There is opportunity to pool resources.

Why Yield Mgmt. for On Demand Marginal cost of providing On Demand services is very low, Marginal cost of providing On Demand services is very low, Market for On Demand services is segmentable, with different job requirements and urgencies, Market for On Demand services is segmentable, with different job requirements and urgencies, While mainly large players (IBM, HP,Sun) are touting On Demand now, field will grow to a large number of mid-size providers -> synchronization of pricing is inevitable. While mainly large players (IBM, HP,Sun) are touting On Demand now, field will grow to a large number of mid-size providers -> synchronization of pricing is inevitable.

Yield management: Opt. Model The model to determine optimal yield mgmt. quantities on the IT utility takes as input: User (random) discrete choice preference function describing the probability of a user with workload type accepting a YM offering User (random) discrete choice preference function describing the probability of a user with workload type accepting a YM offering Probability that an arriving job is of that type Probability that an arriving job is of that type Random workload, storage req. of jobs Random workload, storage req. of jobs Characteristics of the resources (node speeds, storage available, memory and CPU available) Characteristics of the resources (node speeds, storage available, memory and CPU available)

Optimization Model (Dube et al. 2005) T : sojourn time of a job in the system; r and p : unit prices/segments for compute power and storage space; P: choice probability function; : probability of arrival of a customer of type c c=customer type, i=time, k=fee, q=machine type nonconcave, nonlinear Degree of nonconcavity related primarily to the choice of sojourn time function for each job the choice of sojourn time function for each job the discrete choice model of customer behavior the discrete choice model of customer behavior

Customer Choice Models Customer (dis)utility with class i: Customer (dis)utility with class i: Weighted Utility Weighted Utility Logit Probability Logit Probability

Prior Works P. Dube, Y. Hayel, L. Wynter (2005) P. Dube, Y. Hayel, L. Wynter (2005) A model for yield management of computational resources with exogenous sojourn times. A model for yield management of computational resources with exogenous sojourn times. Objective function with two classes and logit probability Objective function with two classes and logit probability

A Reduction to a Single Period Problem At each decision epochs, the market demand and parameters in customer choice functions are updated At each decision epochs, the market demand and parameters in customer choice functions are updated An optimization problem is solved with new data and the optimal allocation of aggregate CPU to different classes is determined An optimization problem is solved with new data and the optimal allocation of aggregate CPU to different classes is determined We neglect any demand overlap between periods We neglect any demand overlap between periods

Expression for Sojourn Times We need a characterization of We need a characterization of The probability depends on which in turn depends on The probability depends on which in turn depends on Intituitively should depend on Intituitively should depend on  the processing speed of class k, i.e., (larger the smaller is ) (larger the smaller is )  the fraction of demand seen by k, i.e., We use queueing theoretic formulations to express as a function of and We use queueing theoretic formulations to express as a function of and FIFO service discipline at each class k FIFO service discipline at each class k

The Fixed Point Problem For each feasible allocation, the customer choice probability can be characterized as a solution to a system of fixed point equations: For each feasible allocation, the customer choice probability can be characterized as a solution to a system of fixed point equations: Existence and Uniqueness of Probability vector is established Existence and Uniqueness of Probability vector is established  For both the weighted utility and logit probability

Single Period Problem (weighted utility) An example An example

Single Period Problem (weighted utility): choice probability An example An example

Single Period Problem (weighted utility): sojourn times Sojourn Times Sojourn Times

Conclusion and Future Work Yield management for IT resources Yield management for IT resources Transaction duration has an implicit dependence with the processing speed of the class. Transaction duration has an implicit dependence with the processing speed of the class. A model to express the sojourn time as a function of system resources and the market size A model to express the sojourn time as a function of system resources and the market size The formulation should be generalized to account for demand dependency across periods The formulation should be generalized to account for demand dependency across periods

Induced Demand Curve The expected quantity that would subscribe to the IT service based on multi-variate logit model at a given price and quality, all other data being fixed. The expected quantity that would subscribe to the IT service based on multi-variate logit model at a given price and quality, all other data being fixed.

Optimal Yield Management Solution Increase in revenue as the number of price segments increases Increase in revenue as the number of price segments increases Tradeoff in increasing complexity due to a high number of price segments is balanced by a little increase in revenue. Tradeoff in increasing complexity due to a high number of price segments is balanced by a little increase in revenue.

Yield Management for Transactions at a Service Center Total demand over time; Revenue with a single (high, med, low) price vs. 5 price segments

Optimal Number of Price Segments Vs. Demand

Optimal Number of Price Segments Vs. Demand (contd.) Optimal number of price segments is not monotone in demand Optimal number of price segments is not monotone in demand Yield management system should be re-run as new and better demand data become available Yield management system should be re-run as new and better demand data become available

Summary and conclusions Revenue theoretically increases in this type of market with an increasing number of price segments. Revenue theoretically increases in this type of market with an increasing number of price segments. In the optimization model, with discrete choice preference functions (instead of a single demand curve, d(p), behavior is more complex: In the optimization model, with discrete choice preference functions (instead of a single demand curve, d(p), behavior is more complex: Ideal number of segments varies with demand; Ideal number of segments varies with demand; Program must be rerun periodically to optimize revenue. Program must be rerun periodically to optimize revenue. Additional work needed to smooth end-ser price over usage horizon; various financial instruments (options, futures) may be of value. Additional work needed to smooth end-ser price over usage horizon; various financial instruments (options, futures) may be of value.