Dynamic Cloud Pricing for Revenue Maximization

Abstract

• We study the infinite horizon dynamic pricing problem for an infrastructure

cloud provider in the emerging cloud computing paradigm. The cloud

provider, such as Amazon, provides computing capacity in the form of

virtual instances and charges customers a time-varying price for the period

they use the instances. The provider’s problem is then to find an optimal

pricing policy, in face of stochastic demand arrivals and departures, so that

the average expected revenue is maximized in the long run. We adopt a

revenue management framework to tackle the problem. Optimality

conditions and structural results are obtained for our stochastic formulation,

which yield insights on the optimal pricing strategy. Numerical results

verify our analysis and reveal additional properties of optimal pricing

policies for the infinite horizon case.

Introduction

• In our previous work, we addressed the problem in a finite horizonsetting. In this work we extend the analysis to consider the infinitehorizon setting, where the optimal price is only a function of thesystem utilization and not a function of time.

• The objective is to maximize the average expected revenue rate inthe limit as time goes to infinity.

• Our contributions in this paper are two-fold. First, we present aninfinite horizon stochastic dynamic program for the revenuemaximization problem in the cloud, with stochastic demand arrivalsand departures. We characterize optimality conditions for theproblem and prove important structural results, such as the mono-tonicity of optimal price and relative rewards. Second, we conductnumerical studies to verify our analysis. The results also revealseveral interesting observations regarding the interplay between thedegree of demand dynamics and the optimal pricing policy.Dynamic pricing is more important and rewarding when theexpected dynamics is significant compared with the system capacity.

EXISTING SYSTEM

• Though static pricing is the dominant strategy today, dynamic

pricing emerges as an attractive alternative to better cope with

unpredictable customer demand.

• The motivation is intuitive and simple:

• Pricing should be leveraged strategically to influence demand to

better utilize unused capacity, and generate more revenue.

• Indeed, Amazon EC2 has introduced a “spot pricing” feature, where

the spot price for a virtual instance is dynamically updated to match

supply and demand as claimed in.

DISADVANTAGES OF EXISTING SYSTEM

• A provider naturally wishes to set a higher price to get a higher profit

margin; yet in doing so, it also bears the risk of discouraging demand in the

future.

• It is nontrivial to balance this intrinsic tradeoff with perishable capacity

and stochastic demand.

PROPOSED SYSTEM

• Cloud computing poses new challenges to solving revenue maximizationproblems. First, little is known about how the spot price is adjusted, andwhat factors are considered in the pricing algorithm, by a real-worldprovider such as Amazon.

• Also, little is known about demand statistics, and how demand reacts toprice changes. In fact, though Amazon publishes its spot price history, veryfew insights are gained on important aspects related to modeling of themarket.

• Second, for a cloud provider, revenue not only depends on the number ofcustomers, but also on the duration of usage.

• Thus, not only the arrival but also the departure of demand is stochastic,and have to be taken into account when collecting revenue. This clearlyadds to the modeling complexity.

• we consider the scenario where the cloud provider with fixed capacityupdates the spot price according to market demand in this paper.

• Our second contribution is that we formulate the revenue maximization

problem as a finite-horizon stochastic dynamic program, with stochastic

demand arrivals and departures. We characterize optimality conditions for

the stochastic problem and prove important structural results.

• We also extend our model to the case with non-homogeneous demand. We

conduct an asymptotic analysis on this more general but difficult problem.

• We prove a surprising result that when the demand arrival and departure

rates are linear with system utilization, i.e., number of existing instances,

the optimal price is only a function of time and is independent of the

system utilization

ADVANTAGES OF PROPOSED SYSTEM

• The optimal pricing policy exhibits time and utilization monotonicity, and

the optimal revenue has a concave structure.

• The fundamental tradeoff between pricing to the future to attract more

revenue from future demand, and pricing to the present to extract more

revenue from existing customers.

Conclusion

• In this paper, we presented an infinite horizon revenue maximization

framework to tackle the dynamic pricing problem in an infrastructure

cloud. The technical challenge compared to previous pricing work is that

prices are charged on a usage time basis, and as a result the demand

departure process has to be explicitly modelled. An average reward

dynamic program is formulated for the infinite horizon case. Its optimality

conditions and structural results on optimal pricing policies were presented.

We showed that the relative rewards as well as the optimal price exhibit

mono-tonicity, which is resonant with previous results [6], [10]. We also

conducted numerical studies to verify the analysis, and illustrated the

importance of dynamic pricing especially in the strong demand dynamics

scenarios.

System Configuration

• Hardware Configuration

• Processor - Pentium –IV

• Speed - 1.1 Ghz

• RAM - 256 MB(min)

• Hard Disk - 20 GB

• Key Board - Standard Windows Keyboard

• Mouse - Two or Three Button Mouse

• Monitor - SVGA

• Software Configuration

• Operating System : Windows XP

• Programming Language : JAVA

• Java Version : JDK 1.6 & above.

• Back end :MY SQL

Modules

Class diagram

user

+username+password

+registration()+view profile()+give rating()+view rating()+logout()

admin

+username+password

+add category()+add service()+rating()+logout()

Use case

user

register

login

view profile

give rating

view rating

add category

add service

rating

logout

admin

Deployment diagram home

useradmin

login

view profile

give rating

add category

add service

rating

view rating

logout

Activity diagram

home

useradmin

login

view profile

give rating

add category

add service

rating

view rating

logout

Sequence diagram

user system admin

register

login

view profile

give rating

view rating

logout

login

add category

add service

rating

logout

Collaboration diagram

adminuser system

1: register2: login

3: login

4: view profile

5: add category

6: give rating

7: add service

8: view rating

9: rating

10: logout

11: logout

State chart diagram

home

user admin

login

view profile

give rating

add category

add service

rating

view rating

logout

start

stop

Component diagram

home

register nodereceiver

sender

sending

packets

receive feed

back

receive

packets from

send

packets to

receive packets

from before

node

receive

packets

send feed

back

deliver

packets

logout