Abstract
They include [1][2][3] on energy consumption, [1][4][5][6] on throughput, [3][4][5][7][8] on delay, and [3][4][7][8][9][10][11][12] on packet loss rate. The considered stack parameters include packet inter-arrival time [4][6][10][13], packet length [1][2][5][14], transmission power [10][11][13], queue size [7], MAC layer parameters such as maximum (re-)transmission times and retry delay [3][6][7][12], and other physical layer parameters including RSSI [9][10][11][13][14], distance [4][5][11] and interference [1][13].
[1] On Packet Size and Error Correction Optimizations in Low-power Wireless Networks - IEEE SECON, 2013.
[2] DPLC: Dynamic Packet Length Control in Wireless Sensor Networks - IEEE INFOCOM, 2010.
[3] pTunes: Runtime Parameter Adaptation for Low-power MAC Protocols - ACM IPSN, 2012.
[4] Performance Study of IEEE 802.15.4 using Measurements and Simulations - IEEE WCNC, 2006.
[5] Wireless Sensor Networks: Performance Analysis in Indoor Scenarios - EURASIP, 2007.
[6] Adaptive IEEE 802.15.4 MAC for Throughput and Energy Optimization - IEEE DCOSS, 2013.
[7] On the Delay Performance in a Large-scale Wireless Sensor Network: Measurement, Analysis, and Implications - IEEE/ACM Trans. on Networking, 2015.
[8] Measurement-based Analysis of the Effect of Duty Cycle in IEEE 802.15.4 MAC Performance - IEEE MASS, 2013.
[9] Measurement and Analysis on the Packet Delivery Performance in a Large-scale Sensor Network - IEEE INFOCOM, 2013.
[10] Does Wireless Sensor Network Scale? a Measurement Study on Greenorbs - IEEE INFOCOM, 2011.
[11] ATPC: Adaptive Transmission Power Control for Wireless Sensor Networks - ACM SenSys, 2006.
[12] The MAC Unreliability Problem in IEEE 802.15.4 Wireless Sensor Networks - ACM MSWiM, 2009.
[13] Understanding the Causes of Packet Delivery Success and Failure in Dense Wireless Sensor Networks - ACM SenSys, 2006.
[14] On the Mechanisms and Effects of Calibrating RSSI Measurements for 802.15.4 Radios - IEEE EWSN, 2010.
Setting Related
The objective of the paper is to investigate the joint effects of multiple stack parameters on the performance and the performance trade-offs, via a parameter space exploration.
Specifically, they comprehensively investigate the effects of $7$ typical parameters from PHY, MAC and Application Layer on the performance in terms of energy efficiency, throughput, delay and loss.
They employed a sender-receiver pair of TelosB motes, each equipped with a TI CC2420 radio using the IEEE 802.15.4 stack implementation in TinyOS.
The IEEE 802.15.4 standard, specifies both Physical (PHY) and Medium Access Control (MAC) layer parameters.
At the PHY layer, the radio CC2420 achieves a data rate of $250$ kb/s using O-QPSK in the ISM band of $2.4$ Ghz.
At the PHY layer are the distance ($d$) between nodes and the transmission power level ($P_{tx}$).
At the MAC layer are the maximum number of transmissions ($N_{maxTries}$), the retry delay time for a new re-transmission ($D_{retry}$), and the maximum queue size ($Q_{max}$) of the queue on top of the MAC layer used to buffer packets when they are waiting for (re-)transmission.
At the Application layer are the packet inter-arrival time ($T_{pit}$) and the packet payload size ($l_{D}$). Table I gives a summary of these parameters and their value ranges as well as the rationales behind the considered values.
| Layer | Parameters | Parameter values Rationale | |
|---|---|---|---|
| App | $T_{pit}$ - packet inter-arrival time (ms);$l_D$ - packet payload size (bytes) | {10, 15, 20, 25, 30, 35, 40, 50}{20, 35, 50, 65, 80, 95, 110} | Small $T_{pit}$ is selected to create high traffic arrival rate;The maximum payload size for the used radio stack is $114$ bytes. |
| MAC | $Q_{max}$ - maximum queue size (packets);$N_{maxTries}$ - maximum number of transmissions;$D_{retry}$ - retry delay (ms) | {1, 30, 60}{1, 3, 5}{30, 60} | The values represent no queue, medium and large queue;$5$ attempts are enough in our worst channel condition;Two different values are chosen to test the effect of retry delay. |
| PHY | $P_{tx}$ - transmission power level;$d$ - distance between nodes (meter) | {3,7,11,15,19,23,27,31}{10, 15, 20, 25, 30, 35} | CC2420 provides $8$ output power levels;The maximum distance in the experiment scenario is $35$ m. |
Equations and Modeling
- Definition of packet error rate $PER$
$
PER = \frac{Number\ of\ non_ACKed\ transmissions}{Number\ of\ total\ transmissions}.
$
- Definition of energy per bit
$
U_{eng} =\frac{E_{tx} · (l_O + l_D)}{l_D · (1 − PER)}.
$
| Name | Explanation | Notes |
|---|---|---|
| $l_O$ | the stack overhead size | Byte |
| $l_D$ | the packet payload size | Byte |
| $E_{tx}$ | the sending 1 bit data energy | level 31 = $17.4(mA)\times1.8(V)$ |
| $1/U_{eng}$ | the energy efficiency | $\bar{U}_{eng}(mJ/bit)$ |
| $P_{tx}$ | the CC2420 transmission power level |
8 level $\in$ {3,7,11,15,19,23,27,31} |
| Grey zone | $SNR (dB)$ $\in$ $\approx$ $[5,10]$ |
At $35$m, the optimal output power is $11$ for $l_D$ of $110$ bytes while it is $7$ for the other two payload sizes.
The reason is that for large $l_D$, energy consumption for re-transmissions can still be significantly reduced if the link moves from the medium-impact zone into the low-impact zone of $PER$.
When the link is in the “grey zone”, medium-size packets are preferred to minimize energy consumption due to the reduction in re-transmissions for smaller packets. However, when the SNR is above certain threshold ($15.8$ dB for $P_{tx} = 7$), the energy-optimal payload size is the largest payload size considered in the experiment ($110$ bytes).
- Definition of packet error rate
$
PER = \alpha · l_D · exp(\beta · SNR),
$
$\alpha$ = 0.0128 and $\beta$ = −0.15.
- Goodput
Throughput - 链路利用率, 吞吐量, 或每秒的流速 (Byte/second)
Goodput - Throughput的子集, 由有用的流量组成.
goodput 不包括重复包, 将被 downstream 丢掉的包, 或由于无法重组为完整包而要在接收端被丢掉的ATM信元和分组片段等.
They investigate goodput against SNR for different traffic workloads under four typical MAC configurations:
(a) no queue and no re-transmission,
(b) no queue but with re-transmission,
(c) with a queue but no re-transmission,
(d) with a queue and with re-transmission.
$maxGoodput = \frac{l_D}{Tservice} · (1 − PLR_{radio}).$
- Average service time
(1) $T_{SPI}$
– the one-time hardware SPI bus loading time of a data frame;
(2) $T_{frame}$
– the time to transmit a frame consisting of packet payload and overhead;
(3) $T_{MAC}$
– MAC layer delay consisting of two parts: $T_{TR}$ and $T_{BO}$, where $T_{TR}$ is the turn around time (0.224ms) and $T_{BO}$ is the average value of initial back off period (5.28ms);
(4) $T_{ACK}$
– the ACK frame transmission time if ACK frame is received, and based on prior tests $T_{ACK}$ is around 1.96ms;
(5) $T_{waitACK}$
– the maximum software ACK waiting period (8.192ms);
(6) $N_{tries}$
– the number of transmissions to deliver the packet successfully;
(7) $D_{retry}$
– the delay between two consecutive re-transmissions.
Modeling $T_{service}$ and $N_{tries}$ based on the given parameters.
$
\begin{aligned}
&T_{succ} = T_{MAC} + T_{frame} + T_{ACK},\
&T_{fail} = T_{MAC} + T_{frame} + T_{waitACK},\
&T_{retry} = D_{retry} + T_{MAC} + T_{frame} + T_{waitACK}.
\end{aligned}
$
- If $N_{tries} < N_{maxTries}$
$T_{service} = T_{SPI} + T_{succ} + (N_{tries} − 1) · T_{retry}.$
- If $N_{tries} > N_{maxTries}$
$T_{service} = T_{SPI} + T_{fail} + (N_{maxTries} − 1) · T_{retry}.$
- Modeling $N_{tries}$
$N_{tries} = 1 + \alpha · l_D · exp(\beta · SNR),$
$\alpha$ = 0.02 and $\beta$ = −0.18 with $95%$ confidence level.
- Modeling $PLR$
$PLR_{radio} = (\alpha · l_D · exp(\beta · SNR))^{N_{maxTries}},$
$\alpha$ = 0.011 and $\beta$ = −0.145.
- Definition of utilization from queuing theory, denoted by $\rho$:
$\rho$ = $\frac{\bar{T_{service}}}{T_{pit}},$
where $T_{pit}$ packet inter-arrival time (ms).
Summary
Large output power, large queue size and small packet size can reduce both radio loss and queuing loss effectively. Under good channel conditions and low traffic arrival rate, re-transmissions reduce packet loss. However, when the link is in the “grey zone” with high traffic load, the choice of the optimal $N_{maxTries}$ depends on the desired trade-off between the radio loss and queuing loss.