On balancing multiple video streams with distributed QoS control in mobile communications

Transcription

1 On balancng multple vdeo streams wth dstrbuted QoS control n moble communcatons Arjen van der Schaaf, José Angel Lso Arellano, and R. (Inald) L. Lagendjk TU Delft, Mekelweg 4, 68 CD Delft, The Netherlands {arjen, jose}@ubcom.tudelft.nl ABSTRACT We study a flexble and adaptve approach for optmzng resource utlzaton n a moble communcaton system that ncludes compresson and msson of multple ndependent vdeo streams. We focus on how the ndependent streams can be balanced usng dstrbuted control. We present a smple theoretcal model and consder ts optmzaton. From the model we extract analytcal results about dstrbuted control and we dscuss how these results relate to practcal prncples. 1. INTRODUCTION Moble communcaton systems face two partcular challenges: the varablty of the moble channel and the constrant on resources (especally on power consumpton). To tackle these problems, we need low-power hardware and a method to adaptvely optmze the system operaton (cf. [1]). For reasons of manageablty and flexblty [], we want to do the adaptve optmzaton n a dstrbuted way, such that each module only deals wth matters t s really nvolved n. Ths requres specalzed nterfaces between the modules that late the local parameters nto abstract QoS nformaton. In ths way the optmzaton method s formed nto a QoS negotaton procedure (cf. [3]). We study QoS negotaton n a system wth multple ndependent parallel streams. QoS negotaton n a herarchc stack has been studed n lterature (e.g., [4]). Also QoS n parallel streams has been studed (e.g., lambda-control and network QoS). Here we focus on the prncples that can be used to balance multple streams wth dstrbuted control, such that the total system approaches the global optmum. We do not focus on practcal mplementatons, but we study a smplfed theoretcal case. Ths allows us to concentrate on prncples rather than on practcal problems.. MODEL We propose a smple mathematcal model that ncludes only the essental elements necessary to study adaptaton n multple ndependent vdeo communcaton streams usng dstrbuted control (see Fg. 1). 1

2 Applcaton Layer Weght (w ) Vdeo Encoder Vdeo Encoder Vdeo Encoder Encoded varance (V ) Bt-rate (B ) Protocol / Transmsson Layer Fgure 1: Model of the communcaton system. See text for detals. The applcaton layer n our model produces multple vdeo streams, whch are handed to ndependent vdeo encoders for compresson before msson. The applcaton judges the overall qualty usng dfferent weght factors (w ) for each vdeo stream. The ndvdual vdeo encoders form the vdeo nformaton from the applcaton nto a compressed btstream. The compresson sacrfces some of the qualty of the vdeo materal n order to reduce the bt-rate (B ). The qualty of a sngle stream s gven by the encoded varance (V ), whch s the porton of the sgnal varance that s encoded by the bt-stream (whch equals the varance of the orgnal sgnal mnus the varance of the dstorton). Note that n practce the relaton between encoded varance and perceved qualty of a vdeo stream s not trval. In our theoretcal model, however, we wll not consder these detals, but smply use V as an abstracton of qualty. The overall qualty (Q) s gven by the weghted sum over all streams. Q = w V (1) We smplfy the cost functon by latng the usage of computatonal and msson resources nto terms of power usage. For each vdeo stream (assocated wth each vdeo encoder) we have two free parameters: the encoded varance (V, related to the qualty of the stream) and the bt-rate (B ). All other nternal parameters of the vdeo encoder can be derved from these two parameters by nternal power usage optmzaton. Wth ths constrant, V and B determne the power consumpton of encoder, whch s gven by P = f B, V ) () ( The power consumpton of the msson (P ) depends on the total bt-rate. P = g B (3).1 Propertes of the functons f and g In general, power usage of vdeo encodng (gven by the functon f ) ncreases when more varance (V ) s encoded n a vdeo stream (better qualty). Power usage of vdeo encodng

3 also ncreases for obtanng a hgher compresson rato,.e., a lower bt-rate (B ). In contrast, the power usage of msson (gven by the functon g) decreases for lower btrates (ΣB). These propertes are shown n Fgure. (A) (B) (C) f (V, B ) f (V, B ) g(σb) V Fgure : Schematc propertes of f and g B ΣB The power consumpton of encodng (f ) s largely determned by computatonal costs. Note that f we allow frequency and voltage scalng [1], then the power consumpton scales nonlnearly wth computatonal complexty. Also note that the functon f s not separable wth respect to V and B, because the mnmum bt-rate depends on V and the maxmum encoded varance depends on B. The power consumpton of msson (g) s determned ndrectly by computatonal costs (e.g., for modulaton and error correcton components) and drectly by msson power. The requred msson power depends on the bt-rate and on the state of the moble channel.. Optmsaton The method of Lagrange multplers allows us to extract equatons that defne the confguraton that globally optmzes qualty at a fxed power budget (P budget ). We calculate the total power consumpton (P total ) by the sum of the power consumpton of all modules: P = P + P (4) total Note that we neglect the power consumpton of the applcaton layer, whch we assume to be constant, and therefore rrelevant for our model. Usng the qualty measure (Q), the constrant P budget - P total = 0, and a Lagrange multpler λ, we fnd the followng crteron (C). C = Q + λ P budget P ] (5) [ total For the optmzed crteron (5) we fnd: C B = P B P + B 0 λ 0 (6) = P B P = B 3

4 C P 1 P 1 = 0 w λ = 0 = V V w V λ C = 0 P + P Pbudget = 0 P λ + P = P budget (7) (8) Usng the equatons obtaned by the method of Lagrange multplers as a startng pont to develop a dstrbuted control structure ensures that the dstrbuted system wll tend to adapt towards the balanced global optmum. As an example, consder a second order approxmaton of P : 1 1 P = ab + bb + cb V + dv + ev (9) Ths gves wth equaton (6) and (7): = c B V = c 1 P w a + e c d be B λ 1 w P d b c a + be λ B (10) (11) Ths example shows that both B and V depend on P B, w, and λ. 3. DISTRIBUTED CONTROL Based on the Lagrange multplers equatons (6) and (7) we derve a recursve control structure n whch V and B are controlled by ndependent unts (see Fg. 3A). We assume that all parameters have ntal values that are close (but not necessarly equal) to ther optmzed values. The recursve control loop conssts of teratvely updatng the free parameters B and V. Usng equaton (6) we can calculate B, whle keepng all other parameters (V and parameters of other streams) constant. Calculatng B on the bass of (6) requres knowledge of P B and P B as a functon of B. The frst entty ( P B ) depends on the power consumpton of the vdeo encoder module wth respect to bt-rate. We assume that ths knowledge s present n the vdeo-encodng module. The second entty ( P B ) denotes the power consumpton per mtted bt, whch depends on the btrates of other streams, as well as on the state of the moble channel. Ths nformaton s assumed to be present n the msson layer and s communcated towards the vdeoencodng module n order to calculate an of B. The d value of B must be passed back from the encodng module towards the msson layer, frst because t descrbes the workload, and second, because the bt-rate B nfluences the power consumpton of msson ( P B ) of other streams. We dscuss the mutual nfluence of ndvdual streams later n ths chapter. 4

5 (A) (B) Applcaton Layer Applcaton Layer w λ w λ w λ V w λ V V Vdeo Encoder B Vdeo Encoder B, V B P B B P B P B P B Transmsson Layer Transmsson Layer Fgure 3. Dstrbuted control structure for ndvdual streams, (A) usng the equatons (6) and (7) separately, and (B) usng a combned soluton. In the same way we can calculate s of V usng equaton (7). In ths case we need knowledge of P V as a functon of V, whch we assume to be present n the vdeo encoder module, and we need the value of w / λ, whch must be passed from the applcaton layer towards the encodng module. The weght factor w s gven and the Lagrange multpler λ s used to control the power consumpton. The proper value of λ can be obtaned usng the power constrant (8), but we wll dscuss that later n ths chapter. After calculaton of V we pass the back to the applcaton layer, such that t can reckon wth the resultng qualty. Havng two separate controls (one for B and one for V ) may nduce convergence problems when P B V s non-zero. Consder the followng example. Suppose that n the recursve optmzaton procedure the bt-rate B s below ts optmal value. Ths devaton wll make P V bgger than normal f P B V s non-zero and negatve. The control on V wll then try to make P V equal to the desred value w / λ, as descrbed n (7). It wll do so by choosng a value for V that s smaller than normal (assumng that P V s postve; see Fg B. for a justfcaton). Ths wll n turn gve P B a hgher value (less negatve) than normal, because P B V s negatve, whch s compensated by the control on B by choosng B smaller than normal (assumng that P s postve; see Fg A. for a justfcaton). So, we now see that an ntally too B 5

6 low value of B wll reman too low after each recurson. Ths behavor of the two separate controls slows down or even prevents convergence. 3.1 Combned controls Instead of usng two separate controls to adapt B and V, t s also possble to combne both nto a sngle control for each stream (see fgure 3B). In ths case both the parameters B and V, are adapted at the same tme wth respect to both P B and w / λ, solvng equatons (6) and (7) smultaneously. As an example, f we use the second order approxmaton of P, gven n (9), then the d values of B and V are gven by (10) and (11). These solutons do not depend on parameters of other streams drectly. However, because λ depends on the power consumpton of the total system and P B depends on the total bt-rate, they are ndrectly related. These ndrect dependences must be solved teratvely. The parameters that need to be passed between the applcaton layer, the encodng module, and the msson layer are the same n the case of a sngle control unt as for two separate control unts (compare Fg. 3A and 3B). Ths means that both approaches can be mplemented usng the same nterfaces between the modules. The nterfaces may be well defned, but the mplementaton of the control nsde each module s stll flexble. 3. Bt-rate control The bt-rates of all ndvdual streams adapt wth respect to the functon P B, whch specfes the energy consumpton per mtted bt. Ths functon depends on the total bt-rate of all streams together, snce P s a functon of B. So, f one stream adapts ts bt-rate, t ndrectly affects all other streams as well. Ths coupled relatonshp can be solved recursvely by alternately adaptng the streams and updatng the functon P. B Ths scheme wll balance both the bt-rates of the ndvdual streams and the encoded varances, such that the overall qualty s optmzed, provded that the recursve procedure converges. In the case that P B s constant (.e., the power consumpton per mtted bt does not depend on the total bt-rate) there s no couplng between the streams wth respect to bt-rate, and convergence s trval. In the case that P B ncreases steeply wth B the couplng between the streams s very strong. However, n that case, the power consumpton of msson (P ) also ncreases very steeply wth btrate, allowng only small changes of bt-rate wthn the power budget. Ths mples that most of the balance comes from adaptaton of the compresson rate. Note that the functon P B may also change due to varaton n the moble communcaton channel, and that those changes are handled n the same way. In ths case the adaptve control balances power consumpton of compresson wth that of msson. 6

7 Applcaton Layer λ λ P budget P total Vdeo Encoder B, V P Vdeo Encoder B, V P Power Control P P B B Transmsson Layer P B Fgure 4: Power control and correspondng dataflow 3.3 Power control So far, we have consdered λ beng constant and we have tred to balance the system wth respect to equatons (6) and (7) only. However, the parameter λ s not constant, but s related to the power usage of the system. It can be derved from the power usage constrant gven n equaton (8). The relaton between λ and power consumpton, however, s not trval. The calculaton of λ s most readly mplemented usng a recursve power control mechansm. As shown n fgure 4, a power control unt collects power consumpton data from all encoder modules and from the msson layer. The total power consumpton (P total ) s then compared wth the power budget (P budget ). Based on the result of ths comparson, the value of λ s ncreased or decreased. If power consumpton s too hgh, we must lower the crteron C,.e., we must make λ bgger. Ths wll lead through equatons (6) and (7) to a reducton of the bt-rates (B ) and encoded varances (V ), and thus to balance of the overall qualty (Q) wth respect to power consumpton (P total ). 4. DISCUSSION The dstrbuted control system that we propose s capable of achevng the same effcency as global control. Ths s only possble f all dstrbuted control unts have the necessary nformaton. Therefore, n our model, the control unts pass nformaton between modules through well-defned nterfaces. The nformaton that s passed through the nterface s an abstracton of the Qualty of Servce (QoS) of the module. Even f the local control s changed, or propertes of the module are altered, the nterfaces reman the same. In ths way partculartes of the module mplementaton are hdden from other modules. Ths provdes the flexblty and manageablty that we amed for. 7

8 The man care wth dstrbuted control s convergence and stablty. We are confdent about the convergence of our model, because controls on the parameters of ndvdual streams are not drect mutually dependent. They are ndrectly balanced through the msson layer by the dervatve of the msson power and through the applcaton layer usng the Lagrange multpler. In our model we focused on power consumpton and the man balancng mechansm s the power control. Power s consumed n the encoder and msson layer, but t s controlled through the parameter λ n the applcaton layer. The balancng effect between the ndvdual streams s obtaned by usng dervatves of the power consumpton. Many aspects (other than power consumpton) of exstng communcaton systems are not yet covered n our model, e.g., source varatons, latency, bt-errors, and robustness. Includng these aspects wll make the QoS nterfacng between the modules more extensve. 4.1 QoS nterfacng n practce The QoS nterfacng n our model conssts of passng parameters back and forth between the dstrbuted control unts. The parameters that are exchanged, however, are not ndependent. For example, the dervatve of the msson power that s passed forwards to the vdeo encoder module depends on the bt-rate that s passed backwards to the msson layer. Therefore, the parameter passng procedure wll have the characterstcs of a negotaton procedure. A practcal method of QoS negotaton (Automatc Resource Contracts, ARC) s gven n [3]. Ths method prescrbes that one of the modules exposes ts QoS operaton space (ncludng costs and qualty measures), such that the other sde can pck the most sutable contract. Our method matches ARC concepts. 5. CONCLUSION We have proposed a smple theoretcal model that balances the communcaton of multple ndependent vdeo streams wth respect to qualty and power consumpton. We have shown that the system can theoretcally be optmzed usng the method of Lagrange multplers and that ths optmzaton can be mplemented usng adaptve dstrbuted control. The dstrbuted control needs communcaton of necessary nformaton between the ndvdual modules n order to acheve the global optmum. Ths can be done n a welldefned way, such that the nformaton represents an abstracton of the QoS of the modules. Ths provdes flexblty and manageablty. We dscussed how our theoretcal QoS nterfaces relate to a practcal mplementaton method (ARC). REFERENCES [1] T.H. Meng, A.C. Hung, E.K. Tsern, & B.M. Gordon Low-power sgnal processng system desgn for wreless applcatons IEEE Personal Communcatons, June, pp.0-31, 1998 [] H. van Djk, K. Langendoen, & H. Sps ARC: a bottom-up approach to negotated QoS 3rd IEEE Workshop on Moble Computng Systems and Applcaton (WMCSA 000), December 000 [3] ARC H. van Djk, K. Langendoen, & H. Sps Applcaton of ARC n system desgn nd nternatonal symposum on moble multmeda system applcatons (MMSA 000), Nov. 000 [4] M. Ott, B. Mcheltsch, D. Rennger, & G. Wellng An archtecture for adaptve QoS and ts applcaton to multmeda system desgn Computer Communcatons, 1, pp ,