Dynamic Power Management in a Mobile Multimedia System with
Contents
1. characteristics of the service provider We assume that the unit inter arrival time for the MM stream can be any distribution Since the exponential distribution is required by the GSPN modeling technique we use the stage method 14 to approximate the MM stream distribution by using a three stage SR model The MM SR consists of places Pyma Pawo Pummi and Puw and activities 44 4b 4b amp 8 1 f 1 a connected as shown in Figure 5 Given a distribution of the input inter arrival time of the MM stream we can obtain the values of 14 Lb Ls amp and by curve fitting Pmmsgut represents the MM SQ Gum Mark Pym1 Mark Pym2 0 amp Mark Pymepur lt MM buffer size Figure 5 GSPN model for the MM SR and SQ To emphasize the difference between MM applications and other applications which we will denote as normal applications from now on we assume that the request inter arrival time for the normal applications is exponentially distributed The GSPN model for these applications is shown in Figure 6 Thorm Pso Gnorm Mark Psq lt SQ capacity Figure 6 GSPN model for the local SR and SQ Figure 7 shows the GSPN model of a task scheduler and a simple SP which has two different power modes active denoted as a and sleeping denoted as s When the SP is in active mode it can be processing MM applications which is denoted by mode a MM or processing normal applications which2. can see that the system with a buffer size of 4 consumes 40 more power than the system with a buffer size of 6 however in the former case the D and J values are smaller than the given constraints The reason for this is that with insufficient buffer space the SP has to spend extra power to provide a faster service speed This experiment also shows that D J L and the size of the MM buffer are not mutually independent Given three of them we can estimate the fourth one More precisely their relationship can be formulated by equations 4 1 to 4 4 where p is the probability that there are i requests waiting in the queue MM buffer and m and v are the mean value and the variance of the waiting requests in the queue n Si pj m 4 1 i l z 2 Gi m pp v 4 2 i 0 n p 4 3 i 0 0 lt p lt 1 i 1 n 4 4 We are interested in finding the minimum buffer size n that is needed to avoid unnecessary power consumption due to over constraints on D and J This problem can be solved as follows Min n n Subject to i p D 4 5 i l Sim nei 4 6 i 0 n Spk 4 7 i 0 PaL 4 8 0 lt p lt l i l n 4 9 We cannot solve above problem exactly However after some simplification we find that if satisfies inequality relations 4 10 4 12 there will be a set of p which satisfies function 4 5 4 9 n 2 L gt J D 4 D 3 4 10 n 1 n 2 L gt m 2 4 11 n 2 n 1 L gt D 3 D 2 J 4 1
3. client is then automatically transformed into a continuous time Markov decision process CTMDP based on which the optimal PQ management policy is solved 4 Policy optimization The input to our policy optimization algorithm is the required QoS which can be represented by D J L In real applications D delay may be specified in time units J jitter may then be specified in time units or square of time units L loss rate may be specified in real numbers However we do not use these constraints directly in our policy optimization process Instead we convert D and J from the time domain to an integer domain related to the number of requests waiting in the queue Next we remove the L constraint by buffer size estimation based on the relation between L D and J Finally we formulate a linear programming problem that can be solved for optimal PQ management policy which achieves minimum power consumption under the QoS constraints 4 1 Transforming the D and J Constraints We use the average number of waiting requests in the queue to represent the average request delay D and the variance of the number of waiting requests in the queue to represent the request delay variance J We use the probability that the queue is full to represent the loss rate L The rationale behind these representations is Theorem 4 1 which shows the relationship between the request delay and the number of waiting requests in the queue Theorem In a PQ managed s
4. o m oa o e canoes 12 Table 3 SP service speed ms in each p_mode a_mode O m oa e E tow power 10 35 0 Table 4 Comparison between PQ optimized and PD optimized policies Qos PD optimized PQ optimized r r 01 01 2 15 0 55 0 96 1 95 0 86 0 98 9 3 1 1 5 0 1 175 0 80 1 46 1 63 1 00 1 49 6 9 enoa 2 15 0 55 0 96 1 92 2 86 0 98 10 7 L eaog 2 15 0 55 0 96 1 72 4 80 0 97 200 In our experiment because the normal application is not time critical we set the performance constraint of normal application simply as loss rate lt 5 We use different QoS constraints D J L for the linear programming problem We solve LP1 to find the PQ optimized policy We use the procedure in 14 to find the PD optimized policy under the given D constraint If the resulting jitter and loss rate cannot meet the QoS constraints we decrease D and recalculate the PD optimized policy until they meet the constraints The results are shown in Table 4 From the above results we reach the following conclusions 1 Our method can calculate the PQ optimized policy for the MM client for given QoS constraints by solving the LP problem only once while the previous DPM method has to obtain the PD optimized policy for given QoS constraints by solving the LP problem multiple times 2 Our method can obtain the PQ optimized policy that matches the given QoS constraints while the previous meth
5. the GSPN stays in a certain marking Definition A controllable GSPN is a GSPN where all or part of the case probabilities of activities can be controlled by external commands 2 4 Distributed Multimedia System Figure 2 shows a simplified view of a distributed MM system with QoS management 17 The system consists of three components an MM server with a database of multimedia objects and a database of QoS information the transport system that mainly consists of a network of communication channels routers and switches and the MM client which can be a portable personal computer pocket PC or another mobile multimedia devices MM Server MM Client Resources CPU memory etc MM Database MM data QoS Database Figure 2 QoS managed distributed multimedia system Each component has its own local QoS manager The global QoS manager controls the QoS negotiation and renegotiation procedure among the components The procedure can be briefly described as follows The local QoS manager reports the available local resources to the QoS manager The global manager computes the QoS that each component needs to deliver based on the available resources and sends the requirement to the local manager The local manager uses its available resources to enforce the local QoS requirement and keeps on monitoring the local QoS If there is a local QoS violation the local manager sends a request to the global manager who will respond
6. 2 Therefore we obtain an upper bound on the minimum required buffer size Nip Max n m n3 4 13 where 7 2 n3 are the solutions of equations 4 10 4 11 and 4 12 If the allocated buffer size is larger than N p there will not be extra power waste due to over constraining D and J Note that this buffer size estimation is independent of the incoming data rate and the system service rate because we assume that the given QoS constraint D J L can always be satisfied by the optimal policy We have performed experiments to verify our buffer estimation method we set J 1 5 L 5 By using different D values between and 3 5 we estimate the minimum buffer size N using 4 13 Figure 8 shows the comparison between the estimated value and the real value that is obtained by simulation The results show the correctness of our method 12 10 2 e real value m estimated value 0 5 1 5 2 5 3 5 D Figure 8 Comparison of real value and estimated upper bound 4 3 Policy optimization by Linear Programming The PQ management problem is to find the optimal policy set of state action pairs such that the average system power dissipation is minimized subject to the performance constraints for the traditional application and the QoS constraints for the MM application 10 First we give the definition of some variables The reader may refer to 14 regarding how to calculate some o
7. Dynamic Power Management in a Mobile Multimedia System with Guaranteed Quality of Service Abstract In this paper we address the problem of dynamic power management in a distributed multimedia system with a required quality of service QoS Using a generalized stochastic Petri net model where the non exponential inter arrival time distribution of the incoming requests is captured by a stage method we provide a detailed model of the power managed multimedia system under general QoS constraints Based on this mathematical model the power optimal policy is obtained by solving a linear programming problem We compare the new problem formulation and solution technique to previous dynamic power management techniques that can only optimize power under delay constraints and demonstrate that these other techniques yield policies with higher power dissipation by over constraining the delay target in an attempt to indirectly satisfy the QoS constraints In contrast our new method correctly formulates the power management problem under QoS constraints and obtains the optimal solution 1 INTRODUCTION With the rapid progress in semiconductor technology the chip density and operation frequency have increased making the power consumption in battery operated portable devices a major concern High power consumption reduces the battery service life The goal of low power design 1 4 for battery powered devices is to extend the battery service life while meeti
8. Power Managed System Construction and Optimization Proceedings of the International Symposium on Low Power Electronics and Design 1999 11 L Benini A Bogliolo S Cavallucci B Ricco Monitoring System Activity For OS Directed Dynamic Power Management Proceedings of International Symposium of Low Power Electronics and Design Conference pp 185 190 Aug 1998 12 E Chung L Benini and G De Micheli Dynamic Power Management for Non Stationary Service Requests Proceedings of DATE pp 77 81 1999 13 L Benini R Hodgson P Siegel System level Estimation And Optimization Proceedings of International Symposium of Low Power Electronics and Design Conference pp 173 178 Aug 1998 14 Q Qiu Q Wu M Pedram Dynamic Power Management of Complex Systems Using Generalized Stochastic Petri Nets Proceedings of the Design Automation Conference pp 352 356 Jun 2000 15 The QoS Forum Frequently Asked Questions about IP Quality of Service URL http www qosforum com docs faq 2000 16 A Vogel B Kerherv G V Bochmann J Gecsei Distributed Multimedia and QoS A Survey IEEE Multimedia pp 10 19 Summur 1995 17 A Hafid G V Bochmann Quality of Service Adaptation in Distributed Multimedia Application Multimedia System Journal ACM Vol 6 No 5 pp 299 315 1998 18 R G Herrtwich The Role of Performance Scheduling and Resource Reservation in Multimedia Syst
9. arch results can be found in 10 13 In situations where complex system behaviors such as concurrency synchronization mutual exclusion and conflict are present the modeling techniques in 8 10 become inadequate because they are effective only when constructing stochastic models of simple systems consisting of non interacting components In 14 a technique based on controllable generalized stochastic Petri nets with cost GSPN is proposed that is powerful enough to compactly model a power managed system with complex behavioral characteristics It is indeed easier for the system designer to manually specify the GSPN model than to provide a CTMDP model Given the GSPN model it is then straightforward to automatically construct an equivalent but much larger CTMDP model The policy optimization algorithms in 8 10 can thereby be applied to calculate the minimum power policy for the power managed system with delay constraints Many Internet applications such as web browsing email and file transfer are not time critical Therefore the Internet Protocol IP and architecture are designed to provide a best effort quality of service There is no guarantee about when the data will arrive or how quickly it will be serviced However this approach is not suitable for a new breed of Internet applications including audio and video streaming which demand high bandwidth and low latency for example when used in a two way communication scenari
10. e performance constraint i e delay for the normal applications 5 Experimental Results Our target system is a simplified model of a client system in distributed MM system System details are as follows The SR has only a request generation state The average inter arrival time of a traditional request is 50ms The SQ capacity is 3 The average inter arrival time of the MM data is 20ms The SP has two p_modes high power mode and low power mode It takes 0 2J energy to switch from high power mode to low power mode and 0 5J energy to switch from low power mode to high power mode To simplify the model we assume that the time needed for switching is small enough to be neglected In both power modes the SP can process both the MM applications and the normal applications but with different power consumption and speed There is also another scenario in which the SP is not processing any application In this case the service speed of SP is 0 and only a very small amount of power is consumed Therefore in our target system there are three a_modes MM normal and idle Table 2 and Table 3 give the SP power consumption and average service time in each combination of p_mode and a_mode Here we assume that the high power mode is designed specifically for MM application For example in this mode a floating point co processor is used so that the service speed of the MM application increases significantly Table 2 SP power w in each p_mode a_mode
11. ems Operating Systems of the 90s and Beyond pp 279 284 A Karshmer and J Nehmer eds Sprintger Verlag Berlin 1991 19 M A Marsan G Balbo G Conte S Donatelli and G Franceschinis Modeling With Generalized Stochastic Petri Nets John Wiley amp Sons New York 1995 20 UltraSAN User s Manual Version 3 0 Center for Reliable and high Performance Computing Coordinated Science Laboratory University of Illinois 14
12. f hard disks The SP provides services e g computing processing communication data retrieval and storage for service requests coming from applications running on the MM client We divide the applications into two categories the MM applications and the other applications We separate the MM applications because of their distinguishing features as explained below 1 The distribution of request inter arrival times is non exponential which requires special treatment during the modeling process 2 The QoS requirement is only applicable to the MM application 3 The priority of the service requests from the MM application is usually higher than those from other applications MM application Other application Figure 4 Top level GSPN model for the MM client Figure 4 shows the top level GSPN model for the MM client It is divided into three major parts 1 MM service requester SR and service queue SQ The MM SR is used to model the statistical behavior of the input MM stream and the MM SQ is used to model the behavior of the MM buffer The GSPN model is shown in Figure 5 2 Local SR and SQ These are used to model the behavior of request generation and as a buffer for other applications The GSPN model is shown in Figure 6 3 The task scheduler TS and service provider SP The TS is used to represent the mechanism for selecting what request is to be processed next The SP is used to model the power performance
13. f the variables from a given CTMDP model pij Probability that the next system state is j if the system is currently in state 7 and action a is taken g i Expected duration of the time that the system will be in state i if action a is chosen in this state y i Probability that the next state of the system will be i and action a will be taken if a random observation of the system is taken pow System power consumption in state i q_MMBuf Number of unprocessed data in MM buffer ene Energy needed for the system to switch from state i to state j Ar Set of available actions in state i Our LP problem is formulated as follows LP1 Min ai 2 Da Fri pow Ta gt ene Pi 4 14 di a ay _ subject to dua ap ep ane 7 py 0 ieS GG Dui Dia xj T l et gt 0 alli a x 9 MMBuf T lt D ra 2 ri par Dae x q _MMBuf D T lt J 4 15 Equation 4 15 gives the constraint on jitter which is represented by the jitter of q_MMBuf Note that the left hand side of 4 15 does not give the exact jitter of q_MMBuf which is pep are xi q _MMBuf Dina xi q _MMBuf ari Ge 4 16 Equation 4 16 contains nonlinear terms For computational efficiency we opted to use an approximation of jitter so that the resulting mathematical program remains linear Proposition For any set of ie i that satisfies 4 15 the value of 4 16 is less than J Proof To minimize xi q_MMBuf m t we know tht
14. is denoted by mode a norm Taecision Taecision S C Paecision S Paecision P worka MM Trati Tprocess 4 MM O een Pyyork norm Tprocess n0rm Piaie S Tyedecision Tyanish P changing Figure 7 GSPN model for the SP and TS To illustrate how the GSPN in Figure 7 works assume that the initial state of the system is active idle and waiting for a MM application and the MM buffer is empty When a token arrives at Pymeur which means that an MM request has arrived the token in place Piae a MM moves to place Pwoxla MM which represents the state of the SP when it is active and servicing an MM request The duration t of this service is decided by the timed activity Tprocess a MM After time t the token in Pyox a MM moves to place Paecision Which represents the state of SP when it is active and accepting command from the PQ manager After a very short time the token in Paecision a moves to Pas Piae a MM or Piae a norm with probability a a and 1 a a In the controllable GSPN these probabilities are the controllable case probabilities of activity Tuecision Which are to be optimized The rest of the system works in a similar way The mechanism of task scheduling is modeled by the immediate activity Tyecision The PQ manager reads the states of all system components and sends commands to control the task scheduling and the SP state transition The GSPN model of the MM
15. king of a place is arbitrary For example the number of tokens in a place could represent the number of requests awaiting service in one application and a request with a certain priority level in another application This flexibility in the meaning of a marking increases the expressiveness of the GSPN for modeling a wide variety of dynamical systems Activities Activities represent actions that take some amount of time to complete There are two types of activities stochastic timed with an exponential distribution and instantaneous Hallow ovals in Figure 1 represent timed activities Timed activities have durations that impact the performance of the modeled system In GSPN the duration of an activity is always an exponential distribution whose mean value represents the average duration of that activity The inverse of the mean value is called the transition rate of that activity The transition rate of an activity may be different depending on system markings Instantaneous activities represent actions that are completed in a negligible amount of time compared to the other activities in the system Solid vertical lines in Figure 1 represent instantaneous activities Case probabilities represented in Figure 1 by small circles on the right side of an activity model the uncertainty associated with the completion of an activity Each case stands for a possible outcome Definition A 1 A place is called a vanishing place if it is the only input place of a
16. l CMOS Design Kluwer Academic Publishers July 1995 2 M Horowitz T Indermaur and R Gonzalez Low Power Digital Design IEEE Symposium on Low Power Electronics pp 8 11 1994 3 A Chandrakasan V Gutnik and T Xanthopoulos Data Driven Signal Processing An Approach for Energy Efficient Computing 1996 International Symposium on Low Power Electronics and Design pp 347 352 Aug 1996 4 J Rabaey and M Pedram Low Power Design Methodologies Kluwer Academic Publishers 1996 5 L Benini and G De Micheli Dynamic Power Management Design Techniques and CAD Tools Kluwer Academic Publishers 1997 6 M Srivastava A Chandrakasan R Brodersen Predictive system shutdown and other architectural techniques for energy efficient programmable computation IEEE Transactions on VLSI Systems Vol 4 No 1 1996 pages 42 55 7 C H Hwang and A Wu A Predictive System Shutdown Method for Energy Saving of Event Driven Computation Proc of the Intl Conference on Computer Aided Design pages 28 32 November 1997 8 G A Paleologo L Benini et al Policy Optimization for Dynamic Power Management Proceedings of Design Automation Conference pp 182 187 Jun 1998 9 Q Qiu M Pedram Dynamic Power Management Based on Continuous Time Markov Decision Processes Proceedings of the Design Automation Conference pp 555 561 Jun 1999 10 Q Qiu Q Wu M Pedram Stochastic Modeling of a
17. m pa ae xi q _MMBuf T Therefore Vm 4 16 gives the smallest value m From the above proposition we know that for any policy if it satisfies constraint 4 15 then the real jitter of q_MMBuf using this policy is less than constraint J Hence we can use 4 15 instead of 4 16 Figure 9 shows an illustration of g MMBuf distribution when the system is using the PQ optimized policy and the PD optimized policy which in previous work optimizes power only under delay constraint In this example we set the MM buffer size to 8 The average length of the MM buffer is the 11 same for both policies The power consumption of the system using the PD optimized policy is 25 less than that of the system using the PQ optimized policy However the g_MMBuf jitter and loss rate of the system using the PD optimized policy are 3X and 1000X larger than those of the system using the PQ optimized policy In the experimental results we can achieve the same g_MMBuf jitter for the system using PD optimized policy by over constraining the average delay and therefore consuming more power oe 0 5 0 35 0 3 0 4 0 25 0 3 0 2 0 15 0 2 ee 0 1 0 05 0 0 0123456738 012345678 q_MMBuf distribution using q_MMBuf distribution using PD PQ optimized policy optimized policy Figure 9 Comparison of g_MMBuf distribution Notice that in LP1 only the QoS constraint for the MM application was included We can easily add th
18. m marking may be changed by the completion of another activity If the activity has not enabled the new system marking the completion of that activity will not happen and all information related to its previous enabling will be disregarded in the future Marking change Change of system marking is only evaluated when there is an activity completion When an activity is completed one of its cases notice that there may be only one case for the activity is chosen based on the pre defined case probability Then the following steps are taken all of the directly connected input places have their markings i e number of tokens decremented the input places connected through input gates change their markings according to the input gate functions all of the places directly connected to the selected case have their markings incremented the places connected through output gates change their markings according to the output gate functions Definition The reachability set of a GSPN from an initial marking Mo denoted as RS Mp is the set of all possible system markings that can be achieved as a result of a sequence of activity completions 2 3 Controllable GSPN with cost Definition A GSPN with cost is a GSPN model with two types of cost impulse cost associate with marking transitions and rate cost associated with system markings Impulse cost occurs when the GSPN makes a transition from one marking to another Rate cost is the cost per unit time when
19. n instantaneous activity otherwise the place is called a tangible place Input gate Input gates enable disable activities and define the marking changes that will occur when an activity is completed In Figure 1 triangles that point to the activity they control represent the input gates i e L There exist arcs from the places upon which the input gate depends also called input places to the base of the triangle Input gates are annotated with an enabling predicate and a function The enabling predicate is a Boolean function that controls whether the connected activity is enabled or not It can be any function of the markings of the input places The function defines the marking changes to the input places that will occur when the activity is completed If a place is directly connected to an activity such as P and T in Figure 1 this is the same as an input gate with a predicate that enables the activity if there is at least one token in the input place and a function that decrements the marking of the input place Output gate Similar to input gates output gates define the marking changes that will occur when an activity is completed The difference is that output gates are associated with a case In Figure 1 triangles whose base is connected to an activity or a case represent output gates i e O1 The triangles point to arcs that connect to the places affected by the marking changes Output gates are defined only with a function The func
20. ng performance requirements Dynamic power management DPM 5 which refers to the selective shut off or slow down of system components that are idle or underutilized has proven to be a particularly effective technique for reducing power dissipation in such systems A simple and widely used technique is the time out policy 5 which turns on the component when it is to be used and turns off the component when it has not been used for some pre specified length of time Srivastava et al 6 proposed a predictive power management strategy which uses a regression equation based on the previous on and off times of the component to estimate the next turn on time In 7 Hwang and Wu have introduced a more complex predictive shutdown strategy that has a better performance However these heuristic techniques cannot handle components with more than two ON and OFF power modes they cannot handle complex system behaviors and they cannot guarantee optimality As first shown in 8 a power managed system can be modeled as a discrete time Markov decision process DTMDP by combining the stochastic models of each component Once the model and its parameters are determined an optimal power management policy for achieving the best power delay trade off in the system can be generated In 9 the authors extend 8 by modeling the power managed system using a continuous time Markov decision process CTMDP Further rese
21. ns 1 This is the first work to consider power and QoS management in a distributed MM system 2 We present a new system model of an MM client This new model accurately captures the different behaviors of the MM and normal applications running on the MM client 3 The proposed optimization solution considers not only power dissipation and delay but also jitter and loss rate We managed to formulate this problem a linear program by making appropriate transformations on the jitter and loss rate constraints This remainder of the paper is organized as follows Section 2 gives the background on GSPN and MM systems Section 3 presents the system modeling techniques for the PQ managed MM client Section 4 introduces the policy optimization method Sections 5 and 6 give the experimental results and conclusions 2 Background 2 1 GSPN Primitives A GSPN consists of four primitive objects places activities input gates and output gates Figure 1 shows an example of a GSPN model P3 T Figure 1 An example GSPN model Places Circles in Figure 1 represent places Each place may contain zero or more tokens which represent the marking of the place The set of all place markings represents the marking of the system M M also represents the state of the system Only the number of tokens in a place matters In Figure 1 the system marking can be written as P P2 which means that there are one token in P and one in P The meaning of the mar
22. o such as net conferencing and net telephony The notion of guaranteed quality of service QoS comes with the emergence of such distributed multimedia systems QoS represents the set of those quantitative and qualitative characteristics of a distributed multimedia system necessary to achieve the required functionality of an application 15 Three parameters widely used to quantitatively capture the notion of QoS in distributed multimedia systems 15 These parameters are 1 Delay D The time between the moment a data unit is received input and the moment it is sent output 2 Jitter J The variation of the delays experienced by different data units in the same input stream In mathematical formulation J can be defined as the variance of the delay or the standard deviation of the delay 3 Loss rate L The fraction of data units lost during transport In this paper we propose a framework of Power and QoS PQ management PQM of portable multimedia system clients The PQ manager performs both power management and QoS management The multimedia MM client is modeled as a controllable GSPN with cost e g power delay jitter and loss rate Given the constraints on delay jitter and loss rate the optimal PQ management policy for minimum power consumption can be obtained by solving a linear programming LP problem Compared to previous research work on power management and multimedia systems our work has the following innovatio
23. od can only meet the QoS constraints by over constraining the delay requirement which results in larger power consumption 6 Conclusions We have presented a new modeling and optimization technique for Power and QoS management in distributed multimedia systems QoS in this context refers to the combination of the average service time delay the service time variation jitter and the network loss rate We model the power managed multimedia system with guaranteed QoS as a GSPN and the PQ optimal policy is obtained by solving a linear programming problem Because jitter and loss rate are correlated parameters we could not include both of them into the LP formulation directly Instead we removed the loss rate constraint from the LP formulation by estimating the maximum size of the queue that stores the MM data Furthermore the jitter constraint is a non linear function of the variables we wanted to optimize Therefore it could not be directly used in the LP formulation We were able to substitute the original jitter constraint with another linear constraint which we mathematically proved to be correct Previous methods only consider the delay constraint while obtaining the PD optimized policy They can only meet the jitter and loss rate constraints by over constraining the delay Compared to these methods we show that our PQM method can achieve an average of 12 more power saving 13 REFERENCES 1 A Chandrakasan R Brodersen Low Power Digita
24. tion defines the marking changes that will occur when the activity is completed If an activity is directly connected to a place this is the same as an output gate with a function that increments the marking of the place For notational convenience we will use the following notation place names start with P activity names start with T input gate names start with T and output gate names start with O 2 2 Executing GSPN GSPN execution refers to the enabling of activities completion of activities and token movement i e changes of system marking Activity enabling An activity is enabled at a certain system marking M when the enabling predicates of all the input gates connected to it are true and there is at least one token in each place that is directly connected to it In Figure 1 activities T and T are enabled in system marking M P P because for each of them there is only one input place that contains one token Activity T4 is not enabled in M because there is no token in P3 The enabling predicate of I decides the enabling of T Activity completion An instantaneous activity is completed immediately after it is enabled A timed activity is completed if it is enabled for its duration time Every time a timed activity is enabled the duration time is obtained by a random sample of the exponential distribution associated with this activity When a timed activity is enabled but not yet completed the syste
25. to the request by either re allocating the local QoS requirement among the different components or negotiating with the user to adopt a degraded global QoS Because low power design is targeted at electronic components with limited power source we focus on PQ management for the MM client The assumption being that the MM client has a large or infinite power source In this context the local QoS manager of the MM client in Figure 2 will be referred to as the local PQ manager 3 Modeling the PQ Managed Client Only components related to the PQ management problem are shown in this block diagram Although the GSPN formalism can model complex systems with multiple interacting service providers in this paper we use a simple system with a single service provider This is because the focus of this paper is on power and QoS management not on complex system modeling As an example of using GSPN to model a complex power managed system with multiple interacting service providers please refer to 14 Figure 3 gives a simplified block diagram of our PQ managed client MM Buffer MM Stream ji Local application f Request Queue QoS constraints gt Local PQ Manager Figure 3 Block diagram of a PQ managed MM client Service Provider Scheduling Control Power Mode i i i Control i As shown in Figure 3 the MM client consists of a service provider SP that may be a CPU a DSP or an array o
26. ystem if the request loss rate is small enough then D Q A where D is the average request delay Q is the average number of waiting requests in the queue and is the average incoming request speed Furthermore during any time period of length T E d E q T X where E d and E q denote the average request delay and average number of waiting requests in the queue during time T and X is the number of incoming requests in this system during time period T Proof omitted to save space 4 2 Estimating the Buffer Size For the MM client allocating too much memory for the MM buffer is unnecessary and wasteful However we have to make sure that the MM buffer is big enough so that the SP does not need to provide unnecessarily fast service to achieve the given loss rate constraint which would in turn result in undesired power consumption Table 1 shows a simple example Assume a PQ managed MM client and a QoS constraint of D J L 1 5 0 9 0 02 In the first case we set the size of the MM buffer to 4 and solve the optimal policy under the constraints of D and J In the second case we set the size of the MM buffer to 6 and solve the optimal policy under the constraints of the same D and J Then we simulate both policies using UltraSAN and obtain the simulated value of D J L and power consumption P Table 1 Power comparison for systems with different buffer size Cese D 3 iL S e pets 09 00 Yt From the above table we
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