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. 13-16, 2005

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A Queueing Model for Yield Management of
Computing CentersParijat DubeIBM Research,
NY, USA Yezekael Hayel IRISA, Rennes,
FranceINFORMS Annual Meeting, San Francisco,
Nov. 13-16, 2005
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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.
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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.

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Features of On Demand

• 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,
• There is opportunity to pool resources.

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Why Yield Mgmt. for On Demand

• Marginal cost of providing On Demand services is
  very low,
• 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 -gt synchronization
  of pricing is inevitable.

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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
• Probability that an arriving job is of that type
• Random workload, storage req. of jobs
• Characteristics of the resources (node speeds,
  storage available, memory and CPU available)

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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
• ccustomer type, itime, kfee, qmachine type
• nonconcave, nonlinear
• Degree of nonconcavity related primarily to
• the choice of sojourn time function for each
  job
• the discrete choice model of customer behavior

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Customer Choice Models

• Customer (dis)utility with class i
• Weighted Utility
• Logit Probability

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Prior Works

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

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A Reduction to a Single Period Problem

• 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
• We neglect any demand overlap between periods

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Expression for Sojourn Times

• We need a characterization of
• The probability depends on which in turn
  depends on
• Intituitively should depend on
• the processing speed of class k, i.e.,
• (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
• FIFO service discipline at each class k

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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
• Existence and Uniqueness of Probability vector is
  established
• For both the weighted utility and logit
  probability

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Single Period Problem (weighted utility)

• An example

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Single Period Problem (weighted utility) choice
probability

• An example

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Single Period Problem (weighted utility) sojourn
times

• Sojourn Times

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Conclusion and Future Work

• Yield management for IT resources
• 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
• The formulation should be generalized to account
  for demand dependency across periods

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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.

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Optimal Yield Management Solution

• 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.

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Yield Management for Transactions at a Service
Center

• Total demand over time Revenue with a single
  (high, med, low) price vs. 5 price segments

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Optimal Number of Price Segments Vs. Demand
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Optimal Number of Price Segments Vs. Demand
(contd.)

• 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

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Summary and conclusions

• 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
• Ideal number of segments varies with demand
• 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.