Optimal In-Network Packet Aggregation Policy for Maximum Information Freshness

Transcription

1 1 Optimal In-etwork Packet Aggregation Policy for Maimum Information Fresness Alper Sinan Akyurek, Tajana Simunic Rosing Electrical and Computer Engineering, University of California, San Diego Abstract Te Internet of Tings is emerging as more wireless sensor networks get deployed every day, pusing decision making and processing towards te edge onto more constrained devices. In tese constrained networks, using a single packet to transmit small sensed data is an inefficient use of bot bandwidt and energy. Aggregating multiple measurements and packets into a single packet increases efficiency and resource utilization, but it also introduces te problem of deciding wen to transmit aggregated data. In tis work, we sow teoretically tat te classical performance metrics of energy consumption and epiration rate create a balanced tradeoff, were teir combined metric of energy consumption per non-epired measurement is a constant, independent of policy selection. We introduce a new metric, information fresness, and derive an optimal policy to maimize it under bot single op and multi-op cases. We provide a distributed algoritm to implement our optimal policy. Our case studies sow tat our algoritm outperforms state-ofte-art policies by more tan 3.3 for information fresness and reduces energy consumption by more tan 62%. I. ITRODUCTIO AD RELATED WORK Time division multiple access TDMA is one of te most energy efficient ways for resource allocation 1, used in wireless sensor network WS protocols suc as IEEE e 2. Altoug time division enables energy efficiency by turning te radio off during unused periods, aving a fied time slot can be inefficient, especially for small packets. In WSs, were nodes transmit sensor readings to a common sink, it is possible to design te optimal transmission slot lengt. However, if te WS as different types of sensors wit different types of measurements, tis may not be possible and te slot lengt must be over-provisioned. In suc cases, packet aggregation witin te network is a more efficient solution. Multiple measurements from different applications or even different nodes are aggregated into a single packet to maimize te efficiency. Furtermore, transmitting a single packet instead of segregated ones, saves energy, decreases endto-end delay and increases te fresness of information. Various algoritms in te literature consider in network packet aggregation. A disadvantage of small packets is tat tey may eperience a wide range of delays, causing jitter. In 3, te autors propose using aggregation to create larger and fewer packets to mitigate jitter. Tey provide a euristic for real-time applications, yet consider only a single application and optimality is not guaranteed. Anoter application of aggregation is used in Voice over Internet Protocol VoIP 4, were delay and jitter are important for quality of service. Te autors propose a timeout based aggregation policy for te single application of VoIP. Te proposed policy maimizes te number of concurrent calls in te network wile reducing te epiration rate and jitter. Interesting work considered te effect of aggregation on Transmission Control Protocol TCP performance 5. Te results sow tat aggregation increases te total capacity, trougput, and TCP efficiency wile decreasing te end-to-end delay and wireless access times. In 6, a timeout based distributed aggregation protocol is proposed. Timeouts are based on eiter a fied interval or a cascading interval based on te op distance. However, te policies do not consider te different requirements for multiple applications. For a broader look at te literature, see 7. If a node cooses to wait for a long time before transmitting its queue, it can aggregate more measurements into a single packet, increasing its efficiency and reducing its energy consumption, but it also increases te delay of all queued measurements, causing problems for delay sensitive applications, creating a tradeoff between energy and delay. In tis work, we first present teoretical analysis in terms of energy consumption and measurement epiration rate, and sow tat te energy consumption per successful measurement is a constant, independent of te policy selection. Tis means tat any improvement in energy consumption results in an equal degradation on epiration rate and vice versa. To mitigate tis tradeoff, we define a new metric: information fresness or fresness in sort. We define fresness as te time a measurement as left until its epiration deadline. Fresness measures ow new te sensed information is and it affects te total performance negatively once it epires. Fresness of eac measurement can be maimized by transmitting tem rigt after generation, but tis would be very costly from energy consumption and resource utilization perspectives. We provide te optimal transmission policy tat maimizes te total fresness per transmission, tus per energy consumption. We etend our solution to a multi-op solution witout te loss of optimality and provide a distributed algoritm to implement our policy wit low overead. Our case studies sow tat we can increase te information fresness per transmission by a factor of more tan 3.3 wile reducing te energy consumption by 62% compared to te state-of-te-art. II. OPTIMAL POLICY FOR IFORMATIO FRESHESS We consider a multi-op network, were eac node decides wen to transmit te measurements in its queue. We define

2 2 multiple applications tat generate teir own measurements. Eac application as its own generation and deadline requirements. As an eample, in a network wit environmental sensor boards, temperature can be sensed rapidly and as loose deadlines, wereas gas sensors suc as carbon dioide, need a longer time to sense, but are more time critical. A measurement is epired, wen te reception time at te sink eceeds its deadline requirement. We assume tat eac transmission as a fied lengt, fied capacity and consumes fied amount of energy. Te radio is turned off during idle times to save energy. Fresness is te time a measurement as left until its deadline, meaning tat an epired measurement still contributes negatively to te fresness metric. A policy decides wen to transmit a packet tat contains all measurements in its queue, up to te capacity of te packet. We first prove tat it is teoretically impossible to improve energy consumption and epiration rate at te same time, by sowing tat te energy per number of non-epired measurements is independent of te policy. Ten we provide an optimal policy tat maimizes te epected information fresness per packet for bot single op and multi-op cases. A. Teoretical Analysis of Transmission Intervals Let π be a policy tat determines, wen a packet is to be transmitted. For a T number of packet transmissions, were any transmission interval j is of lengt T j, te total time of analysis is T total = T T j. We assume tat te transmission appens at te beginning of te interval and any measurement tat arrives during te transmission cannot be added to te ongoing transmission. If eac packet transmission consumes energy E, te total energy consumption is E total = E T and te average energy consumption is: E avg = E T/ T T j Let D i be te deadline for application i. Witin an inactive interval of lengt T j, te measurements tat arrive witin te last part of D i do not epire, wereas te rest do. Te success ratio SR of packets can be written as follows, were is te number of applications and p i,j t, t, k is te probability of generating k packets witin te last t seconds of te j t interval of lengt t for application i: SR = T k=1 p i,j mind i, T j, T j, k, k T k=1 p i,j T j, T j, kk Finally, te energy consumption per successful measurement is obtained as: E E success = 2 p i,j mind i, T j, T j, kk T 1 T k=1 Assuming tat te average packet generation rate for application i is λ i, te epression can be rewritten as: E success λ i T T E mind i, T j 1 3 Tese tree metrics tell us tat: 1 Energy is minimized by waiting as muc as possible, 2 success ratio is maimized wen te transmission interval is equal to te maimum application deadline value, transmitting as fast as possible, 3 energy per successful measurement is minimized wen T j < D i for all applications and te epression is independent of te T j and policy selection. Tis means tat tere is no meaning in claiming optimality for energy consumption or epiration rate, as any improvement in one metric results in an equal degradation in te oter. Tus, in tis paper, we focus on a new metric of importance: information fresness or fresness in sort. Fresness of a measurement is defined as te amount of time it as left until its deadline: Fresnesst = D i t t gen. B. Single Hop Optimal Policy We start wit a single op scenario, were te source of measurements directly transmit to te sink. We consider random deadlines for eac application, were te probability distribution is given as q i d, wic gives te probability of aving d as te deadline of an individual measurement. We assume tat a single packet requires a fied amount of energy to transmit and is big enoug to old all measurements in te queue. Starting from an arbitrary point of time, we consider te problem of deciding in a predictive and proactive way, ow long to wait before transmitting all measurements in te queue, suc tat te total fresness TF is maimized. T F = ma k=0 l=0 t=0 l + tq i lp i k, tkdtdl 4 Taking te epectations and using λ i,t p i k, tk: T F = ma t=0 k=0 ED i + tλ i,t dt 5 We consider two ways of generating measurements: 1 wit a generation process tat doesn t cange witin te interval tat we are considering, so tat λ i,t = λ i, 2 wit a periodic deterministic process. For te first case, were te rate of measurement generation is time independent witin an interval, 5 reduces to a quadratic function: T F = ma ED i λ i 2 2 λ i T F is concave and te maimum is te mean of its two roots: ED i λ i = = ED i w i 7 λ i Te weigt of application i, w i, is te ratio of λ i to te sum of all arrival rates. Te resulting optimal transmission time tat maimizes te total fresness per transmission is a weigted average of application deadlines. Furtermore, te 6

3 3 transmission time doesn t cange if te generation process stays te same, resulting in a periodically transmitting policy implementable using TDMA scemes. For te second case, te rate of generation is deterministic, were we calculate λ i,t using te Dirac-Delta function: λ i,t = δt nt i Using tis definition, 5 becomes: n=0 ma i + 1 i ED i + T i 8 2 i is defined as /T i. Denoting te remainder of te floor operation as M i, suc tat = i T i + M i : EDi ma T i 2T i We ave a quadratic concave function as in te previous case, and denoting λ i = 1/T i, te optimal solution is: / = 2 + ED i λ i λ i = T H /2+ ED i w i Te result is similar to te continuous case, ecept an etra term of T H, wic is te armonic mean of all T i. C. Multi Hop Optimal Policy We etend our single op policy into a multi-op one, were eac node as its own applications wit teir own deadlines and generation processes. We consider a linear pat to te sink, wic represents a branc of te routing tree. We assume tat aggregated packets are furter re-aggregated wit new information at eac op to maimize te packet usage efficiency. We update our previous definitions to generalize into teir multi-op counterparts by adding an additional inde of, representing te op distance to te sink node. As an eample, 3 represents te number of applications of te node 3 ops away from te sink. H is te total number of ops. We start wit te global optimization problem of maimizing te total fresness per a series of transmission to te sink, were te system as a common period of and individual offsets at eac op of, illustrated in Figure 1. Our optimization variable for multi-op becomes: ma H =1 t=0 ED i, + t λ i,t, dt 10 We consider only a generation process tat doesn t cange witin te interval of analysis, suc tat λ i,t, = λ i,t : H T F = ma ED i, 2 2 λ i, =1 11 Tis is a quadratic concave function, were te maimum can be found troug te partial derivatives: T F H = ED i, λ i, = 0 12 =1 T F k = H λ i, H k = 0 13 = t=0 t= Fig. 1. Multi Hop timings as optimization variables. ote tat 13 as no direct solution. Te only feasible solution would be to assign = 0 to remove 13 completely. Since a zero offset is not pysically possible due to transmission and processing delays, we need to modify our optimization. We impose te constraints of S, were S is te required time for transmission and processing delay. Since te minimization version of te optimization problem is conve, we can easily solve for te optimal point by using te Lagrangian dual, were µ is te K.K.T. multiplier: H L, µ = ED i, 2 2 λ i, + L = H =1 H µ S 14 =1 Taking te partial derivatives, we obtain: ED i, L k =1 = µ H =1 λ i, = 0 15 λ i, H k = 0, k 16 Eq. 16 is now feasible and te solution is possible only if all µ > 0. Due to complementary slackness, if µ > 0, ten te constraint must be at its border, suc tat = S,. Using tis result in te first partial derivative epression 15, we obtain te main transmission period for te wole system: = H =1 ED i, H =1 S λ i, λ i, 17 Tis result means tat te system must transmit wit te same period of, wic is a weigted summation of all deadlines and te nodes sould transmit as soon as tey receive a packet from te previous op witout any additional delay. D. Distributed Solution for Multi Hop Optimal Policy Te optimal solution in 17 requires syncronization and consensus between te nodes. Te best efficiency is obtained if all nodes wake up wit a period of even toug it is not mandatory for te policy to work. Te only node tat requires te value is te fartest node from te sink. We need information flow from sink to te fartest node to calculate. To acieve tis, sink starts an update message wit a time stamp inside, periodically. Te receiving node at = 1 uses te time stamp to calculate S 1 and adds te following values: 1 P 1 ED i,1 λ i,1 R 1 1 λ i,1 1 τ 1 λ i,1 S 1

4 4 Te receiving node at = 2 uses te initial time stamp to calculate S 1 + S 2. It adds its own P 2, R 2 and τ 2 values to te received ones and sends te message to te net op. Tis iteration is repeated until te final node, wic calculates te optimal transmission interval as: = H P τ / H =1 R =1 To maimize efficiency and minimize values, te calculated value can be included in te packets towards sink, so tat all nodes ave te same period. Fig. 2. Single application wit Gaussian random deadlines. III. RESULTS We performed multiple case studies, were we compared our algoritm against two state of te art algoritms: 1 Fied 6: transmits periodically, were te period is te average sampling interval of te applications. We also added two more periods of 2 and 4 of te original period for more comparison, 2 Cascading 6: eac node transmits periodically, depending on te op distance to te sink. We consider tree cases: 1 single op deterministic generation, 2 single op Poisson generation, 3 multi-op Poisson generation. Te simulation is implemented in MATLAB using an event based sceme to capture te timing details of te scenarios. For all scenarios, we provide te results for total fresness per transmission, total energy consumption and epiration ratio. Te energy consumption is calculated by scaling te total number of transmissions wit te energy required to transmit and receive by te radios for te duration of te packet. For a CC-2650, te scale corresponds to 0.3mJ approimately 8. Te radio is ten turned off to save energy until te net transmission. Te simulation runtime is 1 our and te arrival rate is 2 measurements/sec, corresponding to an average of 7200 measurements per application per node. We use various deadlines, eplained in eac case, separately. A. Single Hop - Deterministic Generation For te deterministic single op case, we consider two scenarios: 1 a single application, were te measurement deadlines are determined by a Gaussian random variable; 2 two applications wit constant deadlines. Te results for te Gaussian case is sown in Figure 2. We set te mean at 5 seconds and increase te standard deviation to observe te effect of randomness on performance. Since te epected deadline is fied, te optimal transmission period is also fied, resulting in same energy consumption and fresness across all deviations. Our policy is 1.6 better in terms of fresness and reduces te energy consumption by 62% compared to te closest policy Fied 2s. Te epiration rate increases wit increased randomness, due to iger probability of aving deadline values witin te epiration range. 10% of measurements epire on average using our policy. Te results for te constant deadline case are sown in Figure 3. We set different deadlines for te two applications to observe ow a non-uniform deadline distribution affects te performance. Since te mean deadline is te same across all cases, te optimal transmission period is also te same, leading to same energy consumption and fresness across different deadline pairs. Our policy outperforms in terms of fresness Fig. 3. Two applications wit deterministic deadlines. Fig. 4. Varying number of applications wit Gaussian random deadlines. by a factor of 1.5 and consumes 62% less energy tan te closest policy Fied 2s. However, epiration rate increases rapidly wit increasing deadline diversity. B. Single Hop - Poisson Generation We consider a single op case, were te source node generates measurements using a Poisson process. Te deadlines are determined by a Gaussian random variable: 5, 1. In tis scenario, we increase te number of applications running on te source node, to observe te effect of number of applications on te performance. Te results are sown in Figure 4. Te epected deadline for all applications is te same, resulting in te same optimal transmission period for all cases, resulting in fied energy consumption. Fresness increases wit increasing number of applications since more measurements are generated and can be transmitted. Our policy is 1.52 better in terms of fresness and reduces energy consumption by 60% compared to te closest policy Fied 2s. 8% of measurements epire under our policy. C. Multi-Hop - Poisson Generation For te multi-op scenarios, we set te propagation and processing delay between eac node using a uniform random variable between 0, 500ms to maimize randomness. We consider a scenario, were we vary te number of ops from 1 to 9 for 5 different mean deadline values, wit 2 applications running on eac node. We use a uniform distribution to

5 5 Fig. 5. Information fresness for various policies wit different deadline limits and network sizes. Fig. 7. Energy consumption for te multi-op case. compared to te closest policy Fied 2s. Fig. 6. Epiration rate for te multi-op case. determine te deadline of eac measurement. Te fresness results are sown in Figure 5. Te values on te -ais represents te upper limit of te uniform deadline random variable, wereas te lower limit is 1 seconds. Te results sow tat our policy as te igest fresness value. Te fresness increases wit number of ops, because te number of applications also increases wit network size. Furtermore, fresness also increases wit increasing deadline as epected, as fresness is a measurement of remaining lifetime until deadline. For te D = 5 cases, it can be observed tat tere is a decline in fresness after 6 ops. Tis is due to te fact tat at 6 ops, te average distance to te sink node is 1.5 seconds. Considering tat te average deadline is 3 seconds, tere is a probability of never being able to reac te sink node and tis probability increases wit te number of ops. Our policy is optimal in terms of fresness as epected and outperforms te closest policy Fied 2s by a factor of 3.3 on average. Te epiration rate results are given in Figure 6. Epiration rate decreases wit increasing deadline upper limits due to increased fleibility and increases wit increasing number of ops due to increased propagation and processing delays. Altoug te minimum delay to te sink increases wit increasing network size, te effect is least observable wit our policy since it considers tese distances in te calculation of te optimal transmission period. 22% of measurements epire on average under our policy. Te energy consumption results are given in Figure 7. All oter policies ave fied energy consumption since teir transmission period is independent of te deadline values. For our policy, te energy consumption decreases wit increasing delay as te transmission period is directly proportional to it. Our algoritm as te lowest energy consumption and reduces te consumption on average by 62% IV. COCLUSIO Among network aggregation tecniques, packet aggregation is one of te low-cost tecniques to improve resource utilization efficiency. In tis paper, we first sow teoretically tat classical metrics of energy consumption and epiration rate ave a direct tradeoff and teir combined metric of energy consumption per successful measurement is constant and independent from policy selection. We ten present an optimal policy tat maimizes te information fresness of packets by aggregating multiple measurements from multiple ops into a single packet. We provide a distributed algoritm to implement our optimal policy wit a very low communication overead of O. In case studies, we sow tat we acieve te maimum fresness wit an improvement factor of more tan 3.3 over te state of te art policies wile reducing te energy consumption by more tan 62%. ACKOWLEDGMET Tis work was supported in part by TerraSwarm, one of si centers of STARnet, a Semiconductor Researc Corporation program sponsored by MARCO and DARPA; and in part by SF grant # REFERECES 1 S. J. Marinkovic et al., Energy-efficient low duty cycle mac protocol for wireless body area networks, IEEE Transactions on Information Tecnology in Biomedicine, vol. 13, no. 6, pp , ov Ieee standard for local and metropolitan area networks. Online. Available: standards.ieee.org/findstds/standard/ e-2012.tml 3 P. H. Azevêdo et al., A packet aggregation mecanism for real time applications over wireless networks, in Parallel and Distributed Processing Worksops and Pd Forum IPDPSW, 2011 IEEE International Symposium on, May 2011, pp K. Kim et al., On packet aggregation mecanisms for improving voip quality in mes networks, in Veicular Tecnology Conference, VTC 2006-Spring. IEEE 63rd, vol. 2, May 2006, pp J. Karlsson et al., Impact of packet aggregation on tcp performance in wireless mes networks, in World of Wireless, Mobile and Multimedia etworks Worksops, WoWMoM IEEE International Symposium on a, June 2009, pp I. Solis and K. Obraczka, In-network aggregation trade-offs for data collection in wireless sensor networks, Int. J. Sen. etw., vol. 1, no. 3/4, pp , Jan Online. Available: ttp://d.doi.org/ /ijset E. Fasolo et al., In-network aggregation tecniques for wireless sensor networks: a survey, IEEE Wireless Communications, vol. 14, no. 2, pp , April Cc-2650: Simplelink multi-standard 2.4 gz ultra-low power wireless mcu. Online. Available: ti.com/product/cc2650