G-commerce Computational economies for resource allocation in computational Grid settings Fundamentals Resources are not free Resources are not free For convincing resource owners to federate their resources for the Grid For convincing resource owners to federate their resources for the Grid The relative worth of a resource is determined by its supply and demand for it. The relative worth of a resource is determined by its supply and demand for it. 2 economic models Commodities markets – natural since applications treat resources as commodities Commodities markets – natural since applications treat resources as commodities Auctions – easy to implement Auctions – easy to implement Evaluation criteria Price stability – i.e. fluctuations of price – price stability for scheduling stability Price stability – i.e. fluctuations of price – price stability for scheduling stability Equilibrium – degree to which prices are fair – trustworthiness Equilibrium – degree to which prices are fair – trustworthiness Application efficiency Application efficiency Resource efficiency Resource efficiency

Commodity Markets and Auctions Commodity Markets A third-party (market) sets a price for resources and asks producers and consumers willing to agree to that price A third-party (market) sets a price for resources and asks producers and consumers willing to agree to that price The participants engage in transactions The participants engage in transactions Based on unsatisfied demands and supplies, new prices are set Based on unsatisfied demands and supplies, new prices are set Consumers don’t ask for specific commodity but chooses one out of many equivalents Consumers don’t ask for specific commodity but chooses one out of many equivalents An attempt is made to satisfy all bidders and sellers at a given price An attempt is made to satisfy all bidders and sellers at a given priceAuctions A third-party (auctioneer) collects resources and bids A third-party (auctioneer) collects resources and bids Highest bidder gets a resource per auction round Highest bidder gets a resource per auction round Prices are set based on bids Prices are set based on bids Process repeated for other resources Process repeated for other resources Consumers ask for specific commodities Consumers ask for specific commodities One bidder and one seller satisfied at a given price One bidder and one seller satisfied at a given price

Producer and Consumer Models Producer model CPU CPU Disk Disk Producer will sell all of its remaining capacities at a given price point if it will turn a profit with respect to average profit over time Producer will sell all of its remaining capacities at a given price point if it will turn a profit with respect to average profit over time Consumers and jobs Consumers are given initial budget and periodic allowances Consumers are given initial budget and periodic allowances Budgets are refreshed at periodic intervals Budgets are refreshed at periodic intervals Consumers and producers agree on a price and during each simulated minute, the producer’s revenue is incremented and consumer’s budget is decremented Consumers and producers agree on a price and during each simulated minute, the producer’s revenue is incremented and consumer’s budget is decremented Consumers will place demand only if the capable_rate is >= avg_rate Consumers will place demand only if the capable_rate is >= avg_rate

Producer and Consumer Models Summary Producers consider long term profit and past performance when deciding to sell Producers consider long term profit and past performance when deciding to sell Consumers are given periodic budget replenishments and spend opportunistically Consumers are given periodic budget replenishments and spend opportunistically Consumers introduce work load in bulk at the beginning of each simulated day, and randomly throughout the day Consumers introduce work load in bulk at the beginning of each simulated day, and randomly throughout the day

Commodities market and dynamic pricing Pricing methodology for market economy Pricing methodology should produce a system of price adjustments which bring about market equilibrium Market economy is a system involving producers, consumers, several commodities, supply and demand functions for each commodity determined by the set of market prices for various commodities A unique equilibrium price is guaranteed to exist in this framework

Commodities Commodity prices represented by price vector, p. z j - Excess demand for the j th commodity, i.e. demand minus supply Each z j is a function of all prices p i Smale’s theorem: an equilibrium point with p* such that excess demand vector z(p*) = 0 exists

Commodities Market Formulation A nxn matrix of partial derivatives Smale’s method: With λ same sign as determinant of D z (p), economic equilibrium can be obtained by - Lamda = 1 ; Euler discretization at positive values of t; reduces the process toNewton Raphson method for solving z(p) = 0 Approximate each excess demand function z by a polynomial in p1,p2,…pn Approximate each excess demand function z i by a polynomial in p1,p2,…pn Use partial derivates of the polynomials High polynomial of degree 17 was used This procedure is called first bank of G method

Auctions When an application desires multiple commodities, it places multiple bids on multiple auctions and obtains some of the resources It expends currency on the obtained resources while it waits for other resources Auctions are highly unreliable in terms of pricing and ability to obtain resource – leads to poor scheduling decisions

Simulations of auctions At each time step, CPU and disk producers submit their unused slots, minimum selling price (average profit / slot) to auctioneers Consumers define bid prices based on demand functions and bid on each commodity needed by their jobs Highest bidding customer gets commodity Price of the commodity – average of commodity’s minimum selling price and consumer’s bid price

Simulation experiments 2 scenarios Under-demand – producers can adequately support consumers Under-demand – producers can adequately support consumers Over-demand – consumers wish to buy more resources than available Over-demand – consumers wish to buy more resources than available Simulation setting Under-demand Under-demand 100 consumers to use 100 CPUs and disks Each consumer submitted random number of jobs (between 1 to 100) at every simulated day break 10% chance of submitting new job every time unit Over-demand Over-demand 500 of the same consumers

Market equilibrium – commodity markets: Illustration of equilibrium by Smale’s method

Market equilibrium - auctions Variance in prices due to different prices paid by different bidders increase over time – i.e. price becomes less stable over time Spikes in workload are not reflected in price. Disk prices are identical even though they are plentiful in number – should be low-priced.

Market equilibrium - Summary Smale’s method is appropriate for modeling hypothetical Grid market First bank of G reasonable and implementable approximation Auctioneering attractive from implementation standpoint But does not produce stable pricing or market equilibrium Grid resource allocation decisions based on auctioneering lack fairness Commodities market formulation perform better from the standpoint of Grid as a whole Over-demand case performed similar to under-demand

Efficiency results Utilization of resources from supplier standpoint Number of jobs completed / time unit from consumer standpoint

Other Pricing Models Posted Price Model Special offers to motivate users to utilize unused slots Special offers to motivate users to utilize unused slots Bargaining Model Tender/contract-net model Bid-based proportional resource sharing model Used in cooperative resource sharing environments Used in cooperative resource sharing environments Share-holders model When users are both service providers and consumers When users are both service providers and consumersMonopoly

References / Sources / Credits Wolski, R., Plank, J., Brevik, J, and Bryan, T., G- Commerce: Market Formulations Controlling Resource Allocation on the Computational Grid (PDF), IPDPS 01, March, Buyya et. al. Economic Models for Resource Management and Scheduling in Grid Computing. Concurrency and Computation. Practice and Experience : GridIS: An Incentive Based Grid Scheduling. Xiao et. al. IPDPS 2005 A Game Theory-Based Pricing Strategy to Support Single/Multiclass Job Allocation Schemes for Bandwidth- Constrained Distributed Computing Systems. Ghosh et. al. TPDS 2007.

JUNK!

Differences In commodity markets, an attempt is made to satisfy all bidders and sellers at a given price In auctions, one bidder and seller is satisfied at a given price