1. `Heavily-tailed Network Traffic modeling for a Power Management
Algorithm: Windows Wireless Service
Edwin Hernandez-Mondragon Arun Ayyagri
Motorola Inc, The Boeing Company
8000 W. Sunrise Blvd., P.O. Box 3999,
Plantation, FL, 3332. Seattle, WA 98124-2499
edwin.hernnadez@motorola.com arun.ayyagari@boeing.com
Abstract algorithm based upon renewal processes, this
algorithm optimizes a control policy by monitoring the
Power savings in battery-operated equipment can number of elements in the queue at the mobile host and
be improved by scheduling the active duty cycles on the transition probabilities while in the doze and off
the network card depending upon the current network states. Additional steps should also be taken to
traffic statistics. We conducted analytical experiments improve power utilization by defining a power control
using exponential arrivals to simulate mobile host algorithm that monitors the signal strength value at the
requests and Pareto service rates for the network access point (AP) and the mobile host, as well as the
responses. The results showed that the buffer size must bit error rate (BER). In this approach, the AP performs
be carefully chosen every time the management the calculations for the optimal transmission power to
algorithm schedules a short duty cycle being several be used by the client. Alternatively, in a distributed
orders of magnitude greater than deterministic and computing option, the AP could provide the
exponential values expected. A tradeoff between the information for the power control algorithm to the
average power savings and the probability of mobile host to enable the mobile host to independently
congestion has to be considered especially for heavily determine the optimal transmission power. Their
tailed network traffic patterns. results indicated that for web-browsing applications
the savings could be of around 60% and telnet
1. Introduction applications resulted on savings of up to 80% on the
power used by the card. Additionally, Simunic showed
Power management in network cards is a very that by using Pareto distributions and assuming a self-
important issue for battery-operated equipment [1]. In similar network service times, a greater penalization
general this type of equipment requires tight value was observed in the range of 2-10 seconds.
constraints in terms of energy consumption. Ideally, a On the other hand, the industry has also made
power management algorithm would allow the efforts to improve asynchronous medium access
network card, hard-drive, or any other device to power control protocols like the MAC in IEEE 802.11 [2] and
off, during idle periods of time; and power it on during make them more efficient. Although, as presented by
periods of utilization. Although, the many available E. Takahashi [3], the one-fits all power management
methods for power saving in portable computers are policy found on the IEEE 802.11 standard still has
based upon timeout periods rather than wisely many energy inefficiencies. Takahashi also approached
determining idle periods of time. An average of 20% the issue of power consumption and delay introduced
of the total power consumed by many laptops is due to in IEEE 802.11 networks in order to propose a new
the wireless LAN interface therefore an intelligent MAC protocol. Takahashi’s protocol avoids the
method for power management would improve the life unnecessary receiver idle times by approximation of
in the battery. This paper proposes a new power the ideal fluid model and guarantee communication
management algorithm targeting wireless network services. The combination of a modified version of the
cards and how operating system services, such as Point Coordination Function (PCF) and an explicit
Microsoft Windows, would interact with the network traffic re-shaper function was the key factor for the
card. improvements shown in this paper. The results
Many algorithms have been proposed to improve presented indicate that it is possible to reach savings
the power utilization in wireless devices. Initially T. between 50-90% within the higher and lower
Simunic, et. al., [1] proposed a power management throughput bounds used by the mobile unit.

2. a 3/8 inch (0.81 cm) space between them. Text must be
Some other studies such as [4,5] try to predict the fully justified.
power consumption on the card by using stochastic
methods and neural networks. C. Hwong, et. al., 2. The Wireless Service (WZC) in
implemented an event-driven application which Windows Operating System
introduced two mechanisms for prediction: prediction-
miss correction and pre-wakeup. Both approaches The wireless service [6] provides the layer-2
required of an exponential predictor to determine the functionality aimed at seamlessly connecting to
upcoming idle period of time. Similar work has been infrastructure and ad hoc networks. The service
also conducted on prediction methods involving neural provides a polling mechanism to detect new available
networks [5]. Even though both prediction initiatives networks every 60 seconds (Tscan). In other words, in
were used to determine the code-length and the Signal- between those scan periods the communication can
to-Noise Ratio (SNR) on a DS/CDMA system, the take place depending upon the request made by
same experiments could be used to indirectly applications from the upper layers. Our main
determine the predicted power consumptions. assumption is based upon the ability to reduce power
Finally, many researchers have proposed power cycle during those periods of time in between scan
management algorithms as part of the solution of an periods where the network utilization is
optimization problem using Markov decision probabilistically “low”. The wireless service is in
processes. L. Benini, et. al., [6] provided a novel charge of the card configuration, establishing ad hoc
approach to optimally find the policies that were the and infrastructure network connections and minimizes
solution for a well defined stochastic problem. Their the user intervention in the process of wireless
findings indicate that higher queue lengths lead to configuration, authentication, and security.
smaller power consumptions and that at higher
throughput rates the power savings are minimal. The
difficulties encountered in real implementation 3. Power Status on Wireless Cards
applications of a stochastic optimization are a weak
supporter for this type of solution. As mentioned earlier, the wireless service takes care
Contrary to predictive and stochastic optimization of the process of setting on and off states of the
methods, our approach determines the values of the network card. In order to understand the tradeoff of
idle time by reviewing historic information of the setting the wireless card from “awake” state or
distribution function of the number of elements in the maximum power consumption towards a “doze” state
queue, at the access point and client levels. Assuming or “off” state, several statistical analysis have been
that there is a probability of congestion, the algorithm made in WaveLAN cards [1]
finds the optimal value of power while minimizing the Figure 1. shows a sketch of the transition functions
expected congestion. and how much time is invested between different state
This paper will, at first, introduce the wireless transitions. In general “doze” to “off” transitions are
service in Windows XP and followed by a brief expected to take between 30 to 90 ms, while “off” to
description of the most popular wireless card “doze” 10 to 50ms [1]. While, the time between state
characteristics, in Sections 2 and 3. Section 4 provides transitions from “doze” to “ON” and vice-versa is less
the metrics and the modeling concepts used to than 10 ms and can be considered as negligible [2].
determine the simulation parameters. Section 5 During power savings mode the card will be set
presents the probabilistic power management from “on” to “doze” state and from “doze” to “off”
algorithm. While Section 6 outlines the state. The minimum delay introduced by switching the
implementation issues required in Windows at the card into doze mode is 100 ms.
Network Device Interface Specification (NDIS) level. According to Takahashi, [3] the doze mode
Finally we draw some conclusions and present future represents power savings of more than 90%, however
work items in Section 7. testing conducted at different service rates and network
All printed material, including text, illustrations, throughputs indicated that at 300 kbps the network
and charts, must be kept within a print area of 6-1/2 card behaves as if no power management policies were
inches (16.51 cm) wide by 8-7/8 inches (22.51 cm) being in place. In addition, when the card is in doze
high. Do not write or print anything outside the print mode, there is a high-probability to observe packet
area. All text must be in a two-column format. delay is at least of a 100 ms. which might cause
Columns are to be 3-1/16 inches (7.85 cm) wide, with noticeable delay on several real time applications.

3. Max current
Current
doze
time
{
{
∆Τ1 ∆Τ 2
Figure 1. Doze to max power transition
function for a wireless card
5. Communication Model and Power
Management. Figure 3. State machine for the power
manager for WZC
Once we understand the behavior of the network
cards and as depicted in Figure 2., the ideal case In order to study the probabilistic behavior of the card
scenario, data transmissions occur exactly during the at different rates and arrivals we will assume that the
“on” cycles of the card being powered. Only for the arrivals or request made by the user to the card reflect
period of time where the number of packets received an exponential or Poisson process with λ as the arrival
or transmitted by the card is very small or zero, the rate. Meanwhile, prior research conducted in network
card could be placed into doze mode or turned off to traffic characterization has determined that service
minimize power consumption. time is self-similar and therefore network traffic is
Max current
fractal [7,8,9,10]. One of the main implications of such
findings is the infinite variance for the distribution
probability see Eq.1 and Eq.2
doze F ( x) = P[ X ≤ x] = 1 − (α / x) β ,
α , β ≥ 0, x ≥ α
time
Ton Tidle
Figure 2. Matching service of data requests to
(1)
the power cycles for a wireless card
f ( x) = βα β x − β −1 (2)
For the wireless service in Windows, the transitions
from “off” to the “on” state occur less frequently and The average power is defined by the function of RMS
the power management algorithm should adaptively current and voltage, although we used the values found
select the appropriate duty cycle times and behave in [3] for power “doze” and “on” states. In fact, we
somewhat similar to the duty cycle profile depicted in can calculate theoretical power values for the different
Figure 2. cards available in the market as shown in Table 1.
The state diagram shown in Figure 3 is a simplified Pave = I rms × Vrms
version of the wireless service using the power
(3)
management feature. By default, the wireless card is
set to be in the “on” state and it switches into scan
N
mode every 60 seconds. The shaded state depicts a 1
∑I
2
probabilistic mechanism where the network traffic I rms = i Vrms = Vo (4)
statistics determines the appropriate time to place the
N i =1
card in “doze” or “off” states, depending on the
characteristics of the network and different security The average value for a service time following Pareto
and authentication issues such as IEEE 802.1X. distribution as shown in Eq. 5, represents the discrete
time average, whereas the continuous average is
presented in Eq. 6.

4. and determine the probability of n=0 and the
complement of that probability determines the time to
Table 1. Current values consumed by the be in the ON state. The analysis could also be done
PCMCIA wireless card during different modes with real traffic data and by traversing the sequence of
of operation. inputs by keeping counters of different bins of ni and
Card Mode Average calculating Pr(ni) in linear time.
Current
Cisco Aironet Transmission 450 mA T doze T − T doze
Reception 250 mA Pave = Pdoze + Pon scan (8)
T scan T scan
Power Savings 15 mA
LucentWaveLAN Transmission 285 mA Pave = Pdoze Pr(n = 0) + Pon Pr(n > 0) =
Reception 185 mA (9)
Power Savings 9 mA Pdoze (1 − Pr(n > 0)) + Pon Pr(n > 0))
This value provides the expected value for the service Using Pareto distributions for the service time and
time. Eq. 6 shows that the Pareto distribution is only exponential distribution for the inter- arrival times, we
applicable for values of si greater than α in other can determine the values for Eq. 9 which provide how
words the minimum service time used for the much buffering and therefore probability of congestion
simulation. Since Tscan>>α we could approximate Eq. in case certain amount of time is scheduled for the card
6 to the integral to infinite and reduce the number of to be in “off” state. Additionally Table 2, shows the
calculations. probability models used for arrival and service rates
N N during the “on” and “off” states shown in Figure 4.
s ave = ∑ si p( si ) = ∑ si βα β s i
− β −1
(5) For a Pr(n>0), we need to consider the probability of
i =1 i =1 one or more packets arriving at the access point (or
∞ αβ base station) or the packets generated by the user at
s ave = ∫ βα β s − β −1 ds = (6) the mobile host at any time between 0 to Tscan will not
α β −1 be negligible. In addition, one needs to add the
The algorithm optimizes the average power probability of packets being serviced longer than the
consumption on the card by determining the duty cycle Ton but before Tscan.
probability of the service time to equal an expected
value of save , used to determine the number of average
packets arriving at the access point during “off” mode
and as the maximum number of packets arriving
during an interval in “doze” mode.
Power (W)
q (i ) = 1 / s aveToff |doze (7)
This queue size can be set to a maximum value to
buffer the data before it could be sent to the network
card during the duty cycle of the card (Eq. 7). The
main drawback of this approach relies on the
associated delay affecting real-time applications where
delay can be an inconvenient. This delay will be
exactly equals to the idle value of time calculated by Figure 4. Pr(n) during the duty cycles
the power management algorithm.
In general, the wireless channel will have a Pr[arrivals
Now in terms of power, we would expect that: within 0 to Ton] which has an exponential distribution
Meanwhile, from Ton to Tscan the probability function
• Poff in “off” or “doze” state , if q(i ) =ε , is provided by Pr[service time in Ton to Toff] which
where, ε represents a very small queue size represents the elements queued at the access point and
• Poni in transmitting or receiving mode if some of the packets also being queued at the network
card.
ε < q(i) ≤ Qmax
In order to determine the average power using Eq. 8
and Eq. 9, we can use different network traffic models

5. fact, it can be proved that {Xt} has a Poisson marginal
distribution with mean value of λβα ( β − 1) .
Table 2. Probability models used at each
Therefore this value was used in the model depicted in
interval of time
Figure 6. to determine the average number of elements
Time Model in the buffers at the access point and mobile unit.
0 < T < Ton Exponential arrival at both
wireless channel and mobile
unit buffer 7000
6000
7000
6000
Pareto Service at both wireless 5000 5000
Queue Size
Queue Size
4000 4000
channel and mobile unit buffer 3000
2000
3000
2000
Ton < T ≤ Tscan No arrivals at the wireless
1000
1000
0
0
0 10 20 30 40 50 60 70
channel
0 10 20 30 40 50 60
Time (Sec) Time (S)
But exponential arrival at the (a) Deterministic λ=100, (b) Self-similar λ=100,
mobile unit buffer µ=1000 µ=1000
No arrivals at the wireless
channel (only if doze mode is 30000
25000
30000
25000
used, Tb = 100 ms). 20000 20000
Queue Size
Queue Size
15000 15000
Elements serviced and buffered 10000 10000
at the access point follow
5000 5000
0 0
0 10 20 30 40 50 60 70 0 10 20 30 40 50 60
Pareto distribution. Time (Sec) Time (S)
(c) Deterministic λ=400, (d) Self-similar λ=400,
Therefore at the wireless channel with a duty cycle less µ=1000 µ=1000
than Tscan: Figure 6. Expected queue size using
Pr(n > 0) = Pr(0 < Tarrival < Ton ) Pr(0 < sn ≤ Ton ) (10) deterministic and self-similar models at
different rates of service and arrival vs. Ton.
= (1 − e − λTON ) * (1 − (α / Ton ) β ) (11)
The first term is exponential, while the second one Therefore, Figure 6 shows the queue size of a self-
corresponds to a Pareto distribution. Research similar model and the values expected if a
conducted in network traffic characterization indicates deterministic model were used, as expected the
that an M/G/∞ model closely represent the internet estimation made by the deterministic model would lead
traffic. The average service time for the Pareto to severe congestion
distribution is βα ( β − 1) , for β ≥1 [8, 9].
The associated delay for a case shown in Fig 6.c, when
t =58 s is zero, although the power consumption in this
1
0.8
1
0.8
scenario cannot be improved since more than 90% of
the duty cycle is required to obtain a probability of
Pr [n=0]
Pr [n=0]
0.6 0.6
0.4 0.4
0.2
0
0.2
0
congestion equals to zero. Although feasible, the range
0 10 20 30
Time (s)
40 50 60 0 10 20 30
Time (s)
40 50 60
if we set a buffer size of 5000 bytes will yield an
average delay of 10 seconds with the duty cycle of
(a) α=0.1 sec,β=1.8, (a) α=1,β=1.8, λ=1 p/sec
75%.
λ=0.1 p/sec
1
0.8
1
0.8
6. Case Study: Power Management
Algorithm for Wireless Service
Pr [n=0]
Pr [n=0]
0.6 0.6
0.4 0.4
0.2 0.2
0 0
0 10 20 30 40 50 60 0 10 20 30 40 50 60
Time (s) Time (s)
Under the assumption that Pareto distributions are
(a) α=1 sec,β=1.8, λ=10 (a) α=10,β=1.8, λ=1000 scale-invariant [9], in that the probability that the wait
p/sec p/sec is at leas 2x seconds is a fixed fraction of the
Figure 5. Probability of n=0 at different values probability that the wait is at least x, for any value of
of λ, TON and α x≥α, we can extrapolate the results presented in Figure
6 to any time-scale and bandwidth since they will
The count process { X t }t =0,1, 2,... represents the number reflect a very similar behavior.
of elements in the queues in the system at time t. In

6. Now the idea, in the real implementation tone should algorithm is the ability of WMI to update the statistic
maintain a vector of inter-arrival rates and the counters appropriately7. Main text
probability of those such that λ, µ, and n are matrices 8. Conclusions and Future Work
storing the historic information collected by the WMI.
These vectors of size 1xN represent the distribution of The efficient use of the duty cycle of power on
the inter-arrival rates measured form the card as well wireless cards has a potential benefit of great power
as the number of elements in the queue. Henceforth, savings. The power savings are tightly coupled to the
the elements are sorted such that : λ i < λ i +1 , associated delay and probability of congestion on the
network. We were able to demonstrate that by using a
µ i < µ i +1 and ni < ni +1 , for all values of i. The probabilistic model with self-similar network traffic,
vector n should define nN-1= Qmax while, nN value the queue size and associated latency can be under-
represents the number of elements in the queue whose estimated using simpler traffic models.
value is greater than Qmax. The WMI will be in charge Although it is feasible to provide a power
of updating these vectors by executing network card management algorithm based upon the statistical
queries at certain intervals of time. information of network traffic, the feasibility of
The vectors: λ, µ, and n also provide the depended applying those policies depends greatly on the upper-
vectors for Pr(λ) , Pr(µ), and Pr(n) and compute the layer application. Many isochronous applications could
different parameters for the power management be negatively affected by the process of scheduling the
algorithm. Hence, the process of finding the duty cycle of the network card, although many other
appropriate value of Tidle can be found by using: applications such as email and web-browsing could
efficiently provide enough statistical information to
0. Initialize(WMI, “Exponential”, “Pareto”) reduce the duty cycle, thereby, save power and with a
1. Determine(µave, λave, nave) properly sized buffer, also decrease the probability of
2. Toff = 1/λave congestion at the access point and the mobile host.
3. ε = 1/λave2 Detecting the network traffic type, whether it
4. Ton = 1/µave follows a deterministic, exponential, or Pareto
5. if Toff+Ton ≥ Tscan then distributions is an important factor to improve the
power management strategy. Further studies are
6. find Toff | Pr[n=(Toff + ε)λave) is minimum
required to optimize the algorithm presented here and
otherwise Toff = 0
refine the specification and implementation details to
7. else
define the structures presented in Section 6.
8. Toff = Tscan - Ton
We conclude that we can save as much power as we
9. Wait_Timer(Update statistics, Tj)
want by controlling the duty cycle, but this must be
10. return Toff
driven by the network traffic statistics. Fuzzy-logic
controllers and neural networks could be able to
By determining the average service times, arrival, and
provide more adaptive approaches that may have a
number of elements in the system both received and
greater potential for improvement.
transmitted, we can estimate Toff depending upon the
chosen values for service and inter-arrival times. This 9. Acknowledgements
value will be used as a starting point to further
determine the proper value Toff which provides the This work was performed as part of a summer
minimum power consumption while minimizing the internship sponsored by Microsoft Corporation in
congestion probability, especially when the Ton and Tpff Redmond, WA.
values determined are greater than the scan period.
Once this case is found, using the Pr(n) table it is easy 10. References
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