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Dynamic bandwidth provisioning using ARIMA-based traffic forecasting for Mobile WiMAX
Computer Communications 34 (2011) 99–106
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Dynamic bandwidth provisioning using ARIMA-based traffic forecasting for Mobile WiMAX Hyun-Woo Kim, Jun-Hui Lee, Yong-Hoon Choi ⇑, Young-Uk Chung, Hyukjoon Lee School of Electronics and Information Engineering, Kwangwoon University 447-1, Wolgye-dong, Nowon-gu, Seoul 139-701, Republic of Korea
a r t i c l e
i n f o
Article history: Received 29 September 2009 Received in revised form 20 August 2010 Accepted 20 August 2010 Available online 25 August 2010 Keywords: IEEE802.16 networks Traffic forecasting ARIMA Bandwidth provisioning QoS
a b s t r a c t With fast proliferation of QoS-enabled wireless packet networks, need for effective QoS control is increasing. In this paper, we focus on QoS provisioning in Mobile WiMAX access service network (ASN). We investigate a dynamic bandwidth provisioning method that can help to increase resource utilization. Our approach consists of two stages: traffic forecasting, followed by bandwidth provisioning. For the first stage, we use auto-regressive integrated moving average (ARIMA) model to forecast traffic based on online measurement. For the second stage, we use a bandwidth provisioning scheme that allocates bandwidths depending on the traffic forecasting. We modeled our problem as a Fractional Knapsack Problem for which we used a greedy algorithm in order to find an approximate solution. Through simulation studies with real-world data sets, we found that our approach could increase the bandwidth for the real-time traffic class and guarantee adequate service quality for the nonreal-time traffic class as well, while maximizing resource utilization. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction WiMAX (Worldwide Interoperability for Microwave Access) is an emerging technology that can provide broadband wireless access (BWA) over long distances. Since the IEEE802.16 working group (WG) took up WirelessMAN standard development activities in 1999, two major standards have been finalized: 802.16-2009 [1] and 802.16j-2009 [2]. The former enables the delivery of last mile broadband access as an alternative to the cable and digital subscriber line (DSL) and supports mobility for ubiquitous Internet access as well. It consolidates and obsoletes IEEE Standards 802.162004, 802.16e-2005, 802.16-2004/Cor1-2005, 802.16f-2005, and 802.16g-2007. The latter, known as mobile multihop relay (MMR), is an amendment to [1] and supports multihop relay. One of the challenges in a multiservice system such as mobile WiMAX with heterogeneous types of traffic is that the limited bandwidth has to be efficiently provisioned among multiple traffic types. The Mobile WiMAX is expected to support diverse real-time applications such as videoconferencing, voice-over-IP, online gaming, and 3G/4G-multimedia, demanding different quality of service (QoS) and bandwidths. Both the IEEE802.16 WG and WiMAX Forum have proposed five different QoS classes: (1) Unsolicited Grant Service (UGS); (2) Real-time Polling Service (rtPS); (3) Nonreal-time Polling Service (nrtPS); (4) Best Effort Service (BE); and (5) Extended
⇑ Corresponding author. Tel.: +82 2 940 5590; fax: +82 2 943 2382. E-mail address: [email protected] (Y.-H. Choi). 0140-3664/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.comcom.2010.08.008
rtPS (ertPS). Bandwidths for these classes need to be properly provisioned for efficient use of the limited network resources. A typical provisioning mechanism in practice is to partition the available bandwidth among the different traffic classes. Usually this partitioning is static and set up on a long-term basis. While static provisioning is simple to implement but may lead to poor performance when the traffic patterns do not conform to the partitioning. So far, overprovisioning has been widely used to absorb traffic fluctuations in several networks such as the landline 3G networks. However, massive overprovisioning based on the amount of traffic measured at peak times is inefficient in terms of resource utilization. Dynamic bandwidth provisioning according to the underlying network condition can increase bandwidth utilization and service provider’s revenue. Over the past 10 years, call admission control (CAC) policies based on movable-boundaries [3–5] have attracted a widespread interest as a means to improve the total channel utilization. Haung et al. [3] proposed a movable-boundary scheme that dynamically adjusts the number of channels for voice and data traffic. With this scheme, the bandwidth can be utilized efficiently while satisfying the QoS requirements for voice and data traffic. In [4], a dual threshold bandwidth reservation (DTBR) scheme for a voice and data integrated system was proposed. DTBR scheme enables the complete sharing (CS) of the overall bandwidth, thus leading to an efficient usage of the wireless resources. However, these approaches require an a priori traffic descriptor in terms of the parameters of a deterministic or stochastic model. One disadvantage is that real traffic may not follow the traffic model that they assume.
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Measurement or usage-based adaptive bandwidth provisioning [6–9] has been brought to attention in the literature. Measurement-based approach is CPU, memory, and time consuming in nature, and therefore, a large prediction interval is required to provide sufficient time for control actions. This approach is suitable for time-insensitive control running on a machine with enough computational capacity. In [6,7], the authors proposed dynamic bandwidth reprovisioning mechanisms for the broadband wireless systems such as 3G and 3.5G. In order to reflect the underlying network conditions, they measure the bandwidth utilization and forecast the required bandwidth by applying a bandwidth estimation model (e.g., moving average or Gaussian estimation). Krithikaivasan et al. [8] proposed a sophisticated traffic forecasting and bandwidth provisioning method. A prediction algorithm derived from an auto-regressive integrated moving average (ARIMA) model has been developed for more accurate, dynamic bandwidth provisioning along with some positive results from performance evaluation using various data sets. However, this scheme does not take into account the heterogeneous types of traffic, and therefore, not directly applicable to the multi-class environment. It has been observed that service degradation approaches may increase bandwidth utilization and service provider’s revenue [10–12]. The common goal of the service degradation approaches is to increase bandwidth utilization by lowering the QoS levels of existing users. The work presented in [10] evaluated the effects of service degradation caused by adaptive bandwidth allocation. Although the system performance can be improved by allowing service degradation, the impact of degradation on the QoS of individual users should be considered. In this work, we attempt to find an adaptive bandwidth provisioning method without an assumption on statistical property of the traffic. Our approach consists of two stages: traffic forecasting, followed by bandwidth provisioning. For the first stage, we use ARIMA model to forecast traffic based on online measurement. For the second stage, we use a bandwidth provisioning scheme that allocates bandwidths depending on the traffic forecasting. We modeled our problem as a Fractional Knapsack Problem for which we used a greedy algorithm in order to find an approximate solution. The rest of the paper is organized as follows. An overview of the IEEE802.16 QoS class is summarized in Section 2. In Section 3, we present the overview of the ARIMA modeling of time series along with the identification of ARIMA models for two data sets used in our study. Next, we give an explanation on how to map the optimization problem to a Fractional Knapsack Problem. In Section 4, we evaluate the proposed dynamic bandwidth provisioning scheme with various data sets. Finally, in Section 5, conclusions follow.
2. The IEEE802.16 QoS traffic classes The bandwidth management scheme and its associated QoS parameters of the IEEE802.16 are defined in [1,2]. For media access control (MAC) layer QoS, the IEEE802.16 specifications define five QoS classes: UGS, rtPS, nrtPS, BE, and ertPS. The three main distinguishing factors among these classes are delay sensitivity, packet size fluctuation, and scheduling type. The UGS supports real-time service flows that generate fixed-size data packets on a periodic basis, whose typical example is constant bit rate (CBR) traffic such as voice-over-IP (VoIP) without silence suppression. The rtPS supports real-time service flows that generate variable-size data packets on a periodic basis, whose typical example is a variable bit rate (VBR) traffic such as moving pictures expert group (MPEG) video. The nrtPS supports nonreal-time service flows that require variable-size data packets on a regular basis. It is suitable for bulk data transfer such as high-bandwidth file transfer protocol (FTP). The BE
supports best effort traffic and suitable for bulk and asynchronous traffic flows such as the email. The ertPS supports real-time service flows that generate variable-size data packets on a periodic basis, as was the case for the rtPS, but it adopts the unsolicited method of bandwidth request, as was the case for the UGS. A typical example of service amenable to the ertPS is the VoIP service with silence suppression. Similarly, the Third-Generation Partnership Project (3GPP) and 3GPP2 define four QoS classes for wireless link: conversational, streaming, interactive, and background. The conversational class provides strict delay guarantees, while background class offers no qualitative or quantitative guarantees. It is the best effort class. The conversational and streaming classes are intended for realtime traffic such as voice and video applications. The interactive class is suitable for data transfer that has request–response patterns. These wireless QoS classes will be mapped to open Internet Engineering Task Force (IETF) QoS architectures (e.g., DiffServ and IntServ). For example, taking IEEE802.16 traffic class model and DiffServ framework into account, the expedited forwarding (EF) per-hop behavior (PHB) is a good candidate to be mapped to the UGS and ertPS classes. Examples of QoS mappings can be found in [13,14]. 3. Description of the proposed method This paper deals with appropriate QoS provisioning among four1 different QoS classes. The system under consideration is an integrated voice/data mobile network with real-time multimedia support. The Mobile WiMAX (especially, R6 interface) is the target environment that we used in our experiments. The main focus of our work is to apply the combination of ARIMA model and Fractional Knapsack Problem in QoS provisioning mechanism of WiMAX, which has not been proposed in the literature previously. Furthermore, we propose integration method of ARIMA and Fractional Knapsack Problem in alternating repetition. 3.1. Time series analysis using the ARIMA model Box and Jenkins [15] developed the ARIMA model which combined the AutoRegresive (AR) and Moving Average (MA) models developed earlier with a differencing factor that removes in trend in the data. A nonseasonal ARIMA model is classified as an ARIMA(p, d, q) model, where p is the number of auto-regressive terms, d is the number of nonseasonal differences, and q is the number of lagged forecast errors in the prediction equation. The Box–Jenkins methodology consists of the following three iterative steps. First, we determine whether the time series is stationary or nonstationary. If it is nonstationary, the series is represented by a new series by applying dth difference of the process to be stationary. Second, in order to identify the values of p and q, we examine the autocorrelation function (ACF) and partial autocorrelation function (PACF) of the time series. For the detailed introduction to model identification based on ACF and PACF, the reader is directed to [15]. Third, having determined p, d, and q, the coefficients of the AR and MA terms are estimated using a nonlinear least squares method. Let fX Ut j1 6 t 6 ng, fX Rt j1 6 t 6 ng, fX Nt j1 6 t 6 ng, and fX Bt j1 6 t 6 ng are the time series for which we want to predict their amount, where the subscripts U, R, N, and B stand for UGS, rtPS, nrtPS, and BE, respectively. In order to obtain the four time series, we monitor utilization of the bandwidth provisioned for each traffic class at a regular interval T. The time series of the link 1 We consider UGS, rtPS, nrtPS, and BE. We exclude ertPS for simplification purpose.
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utilization of UGS class, fX Ut g is expressed by previous observations X Utj , and noise term t which typically correspond to external events. The noise processes t are assumed to be uncorrelated with a zero mean and finite variance. The general ARIMA(p, d, q) model has the form
rd X Ut ¼
p X
Uj ðrd X Utj Þ þ t þ
i¼j
q X
t WNð0; r2 Þ:
hj tj ;
ð1Þ
j¼1
We use the concise form of this expression,
UðBÞrd X Ut ¼ hðBÞt ;
ð2Þ 2
p
where U(B) = 1 U1B U2B UpB is the auto-regressive operator of order p, h(B) = 1 h1B h2B2 hqBq is the moving average operator of q, rd = (1 B)d is the dth order difference operator, and B is the backward-shift operator, i.e., Bj X Ut ¼ X Utj ; Bj t ¼ tj . The same mathematical expression can be applied to fX Rt g, fX Nt g, and fX Bt g. We consider two different data sets downloaded from NLANR [16]. Each data set consists of 24-h data sampled at 6-min interval. We divide each data set into four different traffic classes based on the port numbers shown in Table 1. In order to determine the values of p, d, and q, we used the last 80 samples from each traffic class. First, we determine whether or not each sample data set is a stationary time series. Since they were all nonstationary, we obtained the first-order differences of actual time series X Ut , X Rt , X Nt , and X Bt to generate new times series, W Ut ¼ X Ut X Ut1 , W Rt ¼ X Rt X Rt1 , W Nt ¼ X Nt X Nt1 , and W Bt ¼ X Bt X Bt1 . These new time series were found to be stationary for all data sets, and therefore, we set d = 1 in our ARIMA model. Then, we examined the ACF and PACF plots to find the appropriate values of p and q. The mean square error tests indicated that the order of AR and MA components to be within [0, 4]. The values of p, d, and q can be subsequently updated using a set of samples including newly added measurement data. After identifying the model parameters, p, d, and q, we use the minimum mean square error (MMSE) forecast method to make a prediction. We simply use maximum likelihood point estimator to decide our forecast value. We denote the k-step-ahead predicb U . We call the k is the lead time. When k = 1, then we call tion as X tþk it is one-step-ahead prediction. The prediction performance is presented in Section 4. 3.2. Dynamic bandwidth provisioning using Fractional Knapsack Problem The Knapsack Problem has been widely used to model many resource sharing problems. In the standard Knapsack Problem, there is a set of items each with a value and a weight and a knapsack with a given fixed capacity. The objective is to determine the number of each item to include in a collection so that the total weight is less than a given limit and the total value is as large as possible. In the 0/1 Knapsack Problem each item must either be taken or left behind. However, in the Fractional Knapsack Problem each item can be subdivided. In our model, the weight and the value of the items can be regarded as the traffic amount of each class and traffic
Table 1 Traffic classification based on TCP/UDP port numbers. Class
UGS
rtPS
nrtPS
BE
Application
VoIP
FTP, file sharing
Email, Web
Port numbers
1863
Video/audio streaming 6660, 6661
20, 21, 53, 2122, 3830 6346, 6881, 9001, 9875
25, 80
priority, respectively. The capacity of knapsack corresponds to the total bandwidth. Detailed parameters mapping is shown in Table 2. Given a collection of traffic classes G = {g1, g2, . . . , gn}, where each traffic class gi = hvi, wii worth vi, and weight wi bps, our goal is to fill a wireless link with max-capacity of W bps with traffic classes from G, so that the total value of items in the link is maximized. It is allowed to take fraction of any item. Formally, given a filling pattern F = {f1, f2, . . . , fn} where 0 6 fi 6 1 denotes the fraction of the ith item P we take, the value of this pattern is V F ¼ ni¼1 fi v i and the weight of Pn this pattern is W F ¼ i¼1 fi wi . We wish to find a filling pattern F ¼ ff1 ; f2 ; . . . ; fn g such that W F 6 W, and V F is maximized. Let qi = vi/wi be the value per bps (VPB) for item-i, and sort the set of items by their VPB values. Assume that G = {g1, g2, . . . , gn} is such a sorted list. The Fractional Knapsack Problem can be solved by a greedy strategy as shown in following algorithm. Algorithm 1. Fractional_Knapsack (G, n, W) 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: 13:
/* G is already sorted by the VPB values of items. */ F is an array of size n, initialized to all zeros; Aw W; i 1; while Aw > 0 and i 6 n do if Aw P wi then fi 1; else fi Aw/wi; end if Aw Aw fiwi; i++; end while return F;
The output of the above algorithm, F, is an optimal solution. The proposed dynamic bandwidth provisioning scheme reprovisions bandwidth for each traffic class based on a forecasted bandwidth values as well as on the desired solution reflecting traffic priority of each class. The dynamic bandwidth provisioning algorithm is as follows: Algorithm 2. Dynamic Bandwidth Reprovisioning P bU þ X bR þ X bN þ X b B */ 1: /* Note that ni¼1 wi ¼ X tþ1 tþ1 tþ1 tþ1 Pn 2: if i¼1 wi < W then b U W=Pn wi ; 3: BW UGS X i¼1 tþ1 b R W=Pn wi ; 4: X BW nrPS i¼1 tþ1 b N W=Pn wi ; 5: X BW nrtPS i¼1 tþ1 b B W=Pn wi ; 6: X BW BE i¼1 tþ1 7: else 8: Fractional_Knapsack (G, n, W); /* returns F */ 9: /* i 2 G such that UGS, nrPS, nrtPS, BE. */ 10: while i 6 n do bi ; 11: BW i fi X tþ1
12: 13:
end while end if
When the link is underutilized, we provision the bandwidth for each traffic class proportional to the current traffic amount (lines 2–6). It helps in reducing packet drop probabilities of each class by increasing bandwidth to absorb traffic fluctuations. When the link has no room to accept data packets any more, the bandwidth for each class is reprovisioned according to Algorithm 1 to maximize the total value of items in the link. It can maximize the link utilization taking into account the revenue gain of an operator.
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Table 2 Parameters mapping for Fractional Knapsack Problem. Knapsack capacity
Total link bandwidth
Items Weight
Each service class (i.e., UGS, rtPS, nrtPS, BE) Expected traffic amount of each class (applying one-stepbR ; X bN ; X bB bU ; X ahead prediction) X
Value
Relative priority of each class (e.g., BE:nrtPS:rtPS:UGS = 1:2:3:4)
tþ1
tþ1
tþ1
tþ1
4. Experimental results and discussions In this section, performance of the proposed scheme is evaluated in terms of the packet drop ratio and bandwidth gain. We undertook a number of experiments with various data sets downloaded from NLANR [16] with different traffic sources, relative traffic priority, and sampling/action interval. We selected NLANR data sets since they have been widely accepted and used as generic Internet traffic traces. 4.1. ARIMA prediction with real traces We consider two different data sets collected April 23, 2006 (called, data set 1) and April 30, 2006 (called, data set 2), which are Global Positioning System (GPS)-synchronized IP header trace taken at the access link of the University of Auckland. Each data set consists of 24-h data sampled at a 6-min interval. We divide each data set into four different traffic classes based on the port numbers as shown in Table 1. We denote the ARIMA model with the parameters p, d, and q, as ARIMA(p, d, q). In order to determine the values of p, d, and q, we used the last 80 samples from each traffic class. As mentioned in Section 3, the first-order differences
of actual time series, W Ut ¼ X Ut X Ut1 , W Rt ¼ X Rt X Rt1 , W Nt ¼ X Nt X Nt1 , and W Bt ¼ X Bt X Bt1 were found to be stationary for all data sets, and therefore, we determined d = 1 in our ARIMA model. We examined the ACF and PACF plots to find the appropriate values of p and q. For the data set 1, the ACF plots for the last 80 samples indicated the order q of moving average component to be within [1,4] for all the traffic classes. However, the PACF plots suggested different possible orders for p, which turned out to be within [0, 4] for the UGS, nrtPS, and BE traffic classes and [1,3] for the rtPS traffic class. For the data set 2, the parameters p and q are within [1,4] for UGS, rtPS, and BE traffic and [0, 4] for nrtPS traffic class. Figs. 1 and 2 show the behavior of one-step ahead traffic forecast for data sets 1 and 2. The actual traffic values are shown as dotted lines; the corresponding predicted values are superimposed as solid lines. Fig. 3 shows total amount of bandwidth for the real traces (dotted lines) and its corresponding predicted values (solid lines). We assumed that the total link bandwidth is 22.2 Kb/s for data set 1 and 28.9 Kb/s for data set 2, respectively. Notice that the predicted values can capture the actual traffic values well for the four different traffic classes. Being a model based on past observations, the plots of ARIMA lags behind those of measured data. Notice that the predictions cannot follow rapid changes in traffic. Rapid changes tend to be faced often when the offered aggregate traffic load is low as in our two experiments (e.g., 22.2 and 28.9 Kb/s). Advanced forecasting algorithms such as [17,18] may help in these undesirable instants.
4.2. Bandwidth reprovisioning Our goal is to compare the performance of the proposed scheme to the two conventional schemes, static and semi-static provision-
Fig. 1. Observed traffic amount and predictions with the data set measured in April 23, 2006. (a) UGS class, (b) rtPS class, (c) nrtPS class, and (d) BE class.
H.-W. Kim et al. / Computer Communications 34 (2011) 99–106
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Fig. 2. Observed traffic amount and predictions with the data set measured in April 30, 2006. (a) UGS class, (b) rtPS class, (c) nrtPS class, and (d) BE class.
Fig. 3. Observed total traffic amount and predictions. (a) Data set measured in April 23, 2006 and (b) data set measured in April 30, 2006.
ing. In the static provisioning, bandwidth for each traffic class is provisioned statically based on the average traffic amount for each class. Initially we provisioned 0.105 Kb/s for UGS, 15.1 Kb/s for rtPS, 4.9 Kb/s for nrtPS, and 2.1 Kb/s for BE class for data set 1 and 0.113 Kb/s for UGS, 13.5 Kb/s for rtPS, 13.2 Kb/s for nrtPS, and 2.1 Kb/s for BE class for data set 2. In fact, these values are not typical WiMAX data rates, since they are derived from the given data set. In the semi-static provisioning, bandwidth for each traffic class is provisioned statically, but with the priority of each class taken into account. We assume that the relative priority is 1:2:3:4 for BE, nrtPS, rtPS, and UGS class. The experiments were performed over a period of 16 h. The first experiment with data set 1 was performed with the following parameters: the p, d, q values determined in the previous subsection, the sampling interval T = 6 m, the number of samples, n = 80, the reprovisioning interval 6 m, and Fractional Knapsack parameters described in Table 2. The second experiment with data
set 2 was performed with the same parameters as the first experiment except using different p, d, q values. The bandwidth for each of the four traffic classes is reprovisioned according to the proposed scheme (i.e., Algorithm 2), which is based on the predicted bandwidth amount of each class and Fractional Knapsack Problem. We found the appropriate solution for packing the four classes into the given link. The various choices of vi chosen here are: hvBE, vnrtPS, vrtPS, vUGSsi = h1, 1, 1, 1i and h1, 2, 3, 4i. 4.2.1. Packet drops Fig. 4(a) and (b) shows the total packet drop probabilities for the proposed scheme, static provisioning, and semi-static provisioning. For all the schemes, the number of packet drops depends on the offered traffic load. In static provisioning for data set 1, the data loss of 0.673 MB in average was monitored between t = 0 and t = 16 and 0.671 MB in semi-static provisioning. When the proposed reprovisioning scheme was used for data set 1, the
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Fig. 4. Total packet drop probabilities. (a) Data set measured in April 23, 2006 and (b) data set measured in April 30, 2006.
data loss of 0.602 MB in average was observed between t = 0 and t = 16. For data set 2, we observed the data loss of 1.3 MB, 1.15 MB, 0.89 MB in average for static, semi-static, and the proposed scheme, respectively. In most cases, the packet drop probabilities of the proposed scheme is smaller than the two conventional schemes, static and semi-static provisioning. It is evident that even for two different set of vi values (i.e., h1, 1, 1, 1i and h1, 2, 3, 4i), the total amount of the packet drops are the same. Recall that vi values only affect relative ratio of the packet drop probabilities among four different traffic classes. Note that our prediction-based approach shows quite significant packet drop rate as high as 20% for some time intervals. It is due to the experimental conditions of quite low total link bandwidths (i.e., 8 Mb/s for data set 1 and 10.4 Mb/s for data set 2) and relatively heavy offered load as shown in Fig. 3. Although BE traffic suffers most in both vi = h1, 1, 1, 1i or vi = h1, 2, 3, 4i, the gain obtained from saving higher priority traffic enhances the total value of items in the link. In order to have a direct observation on the different treatments on different traffic classes, we show the individual packet drop
probabilities of each traffic class. Fig. 5(a) and (b) presents the packet drop probabilities for the proposed scheme (with two different vi-value sets), static provisioning, and semi-static provisioning. In Fig. 5(a), we observe an average loss of nearly 11.13% for BE, 9.66% for nrtPS, 0% for rtPS, and 19.01% for UGS when static provisioning scheme is used. We observe different packet loss behavior for semi-static provisioning scheme: 15.86% for BE, 2.24% for nrtPS, 5.41% for rtPS, and 3.63% for UGS. The reason why UGS has low loss ratio is that semi-static provisioning scheme provisions bandwidth statically, but takes relative traffic priorities into account. Note that each bar in the graphs shows the probabilities, not absolute value of the lost packets or bytes. Because we initially provisioned relatively small amount for UGS (0.105 Kb/s) and BE (2.1 Kb/s) compared to rtPS (15.1 Kb/s) and nrtPS (4.9 Kb/s), the significant increase or decrease of the loss probabilities of BE and UGS does not imply noticeable increase or decrease of lost packets or bytes. When we look at the loss ratio behavior for the proposed scheme with vi = h1, 1, 1, 1i, we observe that drop probabilities are better compared to static provisioning. On the other hand, the drop
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Fig. 5. Packet drop probabilities per class. (a) Data set measured in April 23, 2006 and (b) data set measured in April 30, 2006.
probability of nrtPS (5.52%) is worse compared to semi-static provisioning while the drop probabilities of BE (8.91%) and rtPS (0.33%) are better compared to static provisioning. We recall here that the total loss ratio from the proposed scheme mostly lies below that of static and semi-static provisioning scheme as shown in Fig. 4(a) and (b). Because we initially provisioned very small amount for UGS (0.105 Kb/s) compared to rtPS (15.1 Kb/s), nrtPS (4.9 Kb/s), and BE (2.1 Kb/s), the increased amount in the average loss ratio for UGS is actually quite small amount in terms of number of packets. By choosing vi = h1, 2, 3, 4i, we observe that almost the same drop probabilities of UGS and rtPS with vi = h1, 1, 1, 1i case. However, the drop probability of nrtPS decreases to 2.38% while drop probability of BE increases to 18.12%. It is due to the different filling pattern F, which is derived by Algorithm 1. We observe a similar behavior with data set 2 as shown in Fig. 5(b). High BE packet drops may cause many retransmissions and lead to TCP congestion control (e.g., slow start). The overall throughput for BE class may decrease, but high packet drop rate for BE class will not sustain. 4.2.2. QoS Satisfaction Index The bandwidth gain is an important measure because it has implications not only for reducing the call blocking probability of the high priority traffic classes but also increasing resource utilization. Since each class has a different priority, the simple bandwidth gain is not an appropriate indication of network resource utiliza-
tion gain. In order to represent the bandwidth gain, we define QoS Satisfaction Index (QSI). It is supplementary information. Let pj(t) denote the packet drop probability of traffic class j at time t where j = 1 for BE, j = 2 for nrtPS, j = 3 for rtPS, and j = 4 for UGS class. The QSI at time t can be expressed as
P4 QSIðtÞ ¼
j¼1 X j ðtÞð1 pj ðtÞÞzj P4 j¼1 X j ðtÞ
;
ð3Þ
where Xj(t) is traffic amount for class j measured at time t and zj is P relative priority among traffic classes and all j zj ¼ 100. Fig. 6(a) and (b) shows the QSI(t) plots for data sets 1 and 2 with vi = h1, 1, 1, 1i and vi = h1, 2, 3, 4i, respectively. As shown in Fig. 6, the QSI(t) plots tend to be in inverse proportion to number of packet drops. Note that the QSI value of the proposed scheme remains high when the offered load is high, but the static and semi-static provisioning schemes show a slight fall as the load increases. As shown in Fig. 6(a), in static provisioning for data set 1, the QSI value is average 94.9% between t = 0 and t = 16 and average 95.1% in semi-static provisioning. Although the amount of data loss is similar in the static and semi-static provisioning (i.e., 0.673 MB for static and 0.671 MB for semi-static), the QSI values show some difference. The reason why semi-static has better performance in terms of QSI is that the high priority traffic such as UGS and rtPS class experienced low data loss. When the proposed reprovisioning scheme is adopted for data set 1, average 96.8% (with vi = h1, 1, 1, 1i)
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low priority class as well. The bandwidth of each traffic class is predicted through ARIMA(p, d, q) model and the bandwidth reprovisioning problem is modeled as a Fractional Knapsack Problem for which we used a greedy algorithm (Algorithms 1 and 2) in order to find an approximate solution. The experiments performed using real link traces showed that the proposed reprovisioning scheme enables the total number of packet drops to be reduced and QoS Satisfaction Index (QSI) to be increased. As shown in our experimental results, while our approach works quite well most of the time, it is not perfect. The difficulties remain whenever an extremely unexpected turn in traffic is faced. The reprovisioned bandwidth for each traffic class can be used as an essential input to a CAC entity in Mobile WiMAX system. For example, a CAC entity may accept or deny a new VoIP call request based on the reprovisioned UGS bandwidth. Acknowledgments This work was supported in part by the IT R&D program of MKE/ KEIT [KI002084, A Study on Mobile Communication System for Next-Generation Vehicles with Internal Antenna Array] and the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (No. 2010-0027805). References
Fig. 6. QoS Satisfaction Index. (a) Data set measured in April 23, 2006 and (b) data set measured in April 30, 2006.
and 97.0% (with vi = h1, 2, 3, 4i) QSI were observed between t = 0 and t = 16. For data set 2, we observed average 90.8%, 91.9%, 95.6%, and 96.3% QSI in static, semi-static, the proposed scheme with vi = h1, 1, 1, 1i, and with vi = h1, 2, 3, 4i respectively. In summary, the QSI of the proposed scheme is better than the two conventional schemes, static and semi-static provisioning. Although at a specific time interval, static and semi-static provisioning scheme seems to perform well, but in average, the proposed scheme shows a better performance. 5. Conclusions The Mobile WiMAX is expected to support diverse real-time applications such as videoconferencing, voice-over-IP, and online gaming, demanding different QoS and bandwidth. Bandwidths for Mobile WiMAX system need to be properly provisioned for efficient use of the limited network resources. Releasing unutilized bandwidth for use by other services is important for increasing resource utilization. We have investigated how to increase the available bandwidth for high priority class (e.g., UGS) traffic while guaranteeing adequate service quality for
[1] Local and metropolitan area networks, part 16: Air interface for broadband wireless access systems, IEEE Std. 802.16-2009. [2] Part 16: Air interface for fixed and mobile broadband wireless access systems – multihop relay specification, IEEE Std. 802.16j-2009. [3] Y.-R. Haung, Y.-B. Lin, J.-M. Ho, Performance analysis for voice/data integration on a finite mobile systems, IEEE Transactions on Vehicular Technology 49 (2) (2000) 367–379. [4] B. Li, L. Li, B. Li, K. Sivalingam, X.-R.C. Cao, Call admission control for voice/data integrated cellular networks: performance analysis and comparative study, IEEE Journal on Selected Areas in Communications 22 (4) (2004) 706–718. [5] S. Khemiri, K. Boussetta, N. Achir, G. Pujolle, Wimax bandwidth provisioning service to residential customers, in: International Conference on Mobile and Wireless Communications Networks, IEEE, 2007, pp. 116–120. [6] Y.-H. Choi, J. Park, B. Kim, M. Shayman, A framework for elastic qos provisioning in the cdma2000 1xev-dv packet core network, IEEE Communications Magazine 43 (4) (2005) 82–88. [7] B. Al-Manthari, N. Ali, N. Nidal, H. Hassanein, Dynamic bandwidth provisioning with fairness and revenue considerations for broadband wireless communications, in: ICC2008, IEEE Communications Society, 2008, pp. 4028–4032. [8] B. Krithikaivasan, Y. Zeng, K. Deka, D. Medhi, Arch-based traffic forecasting and dynamic bandwidth provisioning for periodically measured nonstationary traffic, IEEE/ACM Transactions on Networking 15 (3) (2007) 683–696. [9] T. Hui, C. Tham, Adaptive provisioning of differentiated services networks based on reinforcement learning, IEEE Transactions on Systems, Man, and Cybernetics – Part C: Applications and Reviews 33 (4) (2003) 492–501. [10] C.-T. Chou, K. Shin, Analysis of adaptive bandwidth allocation in wireless networks with multilevel degradable quality of service, IEEE Transactions on Mobile Computing 3 (1) (2004) 5–17. [11] D. Liao, L. Li, Adaptive service degradation and compensation for multiclass traffic in cdma cellular networks, in: International Conference on Communications, Circuits and Systems, 2006, pp. 1362–1366. [12] S. Das, S. Sen, K. Basu, H. Lin, A framework for bandwidth degradation and call admission control schemes for multiclass traffic in next-generation wireless networks, IEEE Journal on Selected Areas in Communications 21 (10) (2003) 1790–1802. [13] S.I. Maniatis, E.G. Nikolouzou, I.S. Venieris, Qos issues in the converged 3g wireless and wired networks, IEEE Communications Magazine 40 (8) (2002) 44–53. [14] R. Chakravorty, I. Pratt, J. Crowcroft, M. D’Arienzo, A framework for dynamic sla-based qos control for umts, IEEE Wireless Communications (2003) 30–37. [15] G. Box, G. Jenkins, G. Reinsel, Time Series Analysis, Forecasting and Control, third ed., Prentice-Hall, 1994. [16] The national laboratory for applied network research (nlanr) project [online].. [17] B. Krithikaivasan, K. Deka, M. Deep, Adaptive bandwidth provisioning envelope based on discrete temporal network measurements, in: IEEE INFOCOM, 2004. [18] H. ElHag, S. Sharif, An adjusted arima model for internet traffic, in: AFRICON2007, 2007, pp. 1–6.
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Computer Communications journal homepage: www.elsevier.com/locate/comcom
Dynamic bandwidth provisioning using ARIMA-based traffic forecasting for Mobile WiMAX Hyun-Woo Kim, Jun-Hui Lee, Yong-Hoon Choi ⇑, Young-Uk Chung, Hyukjoon Lee School of Electronics and Information Engineering, Kwangwoon University 447-1, Wolgye-dong, Nowon-gu, Seoul 139-701, Republic of Korea
a r t i c l e
i n f o
Article history: Received 29 September 2009 Received in revised form 20 August 2010 Accepted 20 August 2010 Available online 25 August 2010 Keywords: IEEE802.16 networks Traffic forecasting ARIMA Bandwidth provisioning QoS
a b s t r a c t With fast proliferation of QoS-enabled wireless packet networks, need for effective QoS control is increasing. In this paper, we focus on QoS provisioning in Mobile WiMAX access service network (ASN). We investigate a dynamic bandwidth provisioning method that can help to increase resource utilization. Our approach consists of two stages: traffic forecasting, followed by bandwidth provisioning. For the first stage, we use auto-regressive integrated moving average (ARIMA) model to forecast traffic based on online measurement. For the second stage, we use a bandwidth provisioning scheme that allocates bandwidths depending on the traffic forecasting. We modeled our problem as a Fractional Knapsack Problem for which we used a greedy algorithm in order to find an approximate solution. Through simulation studies with real-world data sets, we found that our approach could increase the bandwidth for the real-time traffic class and guarantee adequate service quality for the nonreal-time traffic class as well, while maximizing resource utilization. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction WiMAX (Worldwide Interoperability for Microwave Access) is an emerging technology that can provide broadband wireless access (BWA) over long distances. Since the IEEE802.16 working group (WG) took up WirelessMAN standard development activities in 1999, two major standards have been finalized: 802.16-2009 [1] and 802.16j-2009 [2]. The former enables the delivery of last mile broadband access as an alternative to the cable and digital subscriber line (DSL) and supports mobility for ubiquitous Internet access as well. It consolidates and obsoletes IEEE Standards 802.162004, 802.16e-2005, 802.16-2004/Cor1-2005, 802.16f-2005, and 802.16g-2007. The latter, known as mobile multihop relay (MMR), is an amendment to [1] and supports multihop relay. One of the challenges in a multiservice system such as mobile WiMAX with heterogeneous types of traffic is that the limited bandwidth has to be efficiently provisioned among multiple traffic types. The Mobile WiMAX is expected to support diverse real-time applications such as videoconferencing, voice-over-IP, online gaming, and 3G/4G-multimedia, demanding different quality of service (QoS) and bandwidths. Both the IEEE802.16 WG and WiMAX Forum have proposed five different QoS classes: (1) Unsolicited Grant Service (UGS); (2) Real-time Polling Service (rtPS); (3) Nonreal-time Polling Service (nrtPS); (4) Best Effort Service (BE); and (5) Extended
⇑ Corresponding author. Tel.: +82 2 940 5590; fax: +82 2 943 2382. E-mail address: [email protected] (Y.-H. Choi). 0140-3664/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.comcom.2010.08.008
rtPS (ertPS). Bandwidths for these classes need to be properly provisioned for efficient use of the limited network resources. A typical provisioning mechanism in practice is to partition the available bandwidth among the different traffic classes. Usually this partitioning is static and set up on a long-term basis. While static provisioning is simple to implement but may lead to poor performance when the traffic patterns do not conform to the partitioning. So far, overprovisioning has been widely used to absorb traffic fluctuations in several networks such as the landline 3G networks. However, massive overprovisioning based on the amount of traffic measured at peak times is inefficient in terms of resource utilization. Dynamic bandwidth provisioning according to the underlying network condition can increase bandwidth utilization and service provider’s revenue. Over the past 10 years, call admission control (CAC) policies based on movable-boundaries [3–5] have attracted a widespread interest as a means to improve the total channel utilization. Haung et al. [3] proposed a movable-boundary scheme that dynamically adjusts the number of channels for voice and data traffic. With this scheme, the bandwidth can be utilized efficiently while satisfying the QoS requirements for voice and data traffic. In [4], a dual threshold bandwidth reservation (DTBR) scheme for a voice and data integrated system was proposed. DTBR scheme enables the complete sharing (CS) of the overall bandwidth, thus leading to an efficient usage of the wireless resources. However, these approaches require an a priori traffic descriptor in terms of the parameters of a deterministic or stochastic model. One disadvantage is that real traffic may not follow the traffic model that they assume.
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Measurement or usage-based adaptive bandwidth provisioning [6–9] has been brought to attention in the literature. Measurement-based approach is CPU, memory, and time consuming in nature, and therefore, a large prediction interval is required to provide sufficient time for control actions. This approach is suitable for time-insensitive control running on a machine with enough computational capacity. In [6,7], the authors proposed dynamic bandwidth reprovisioning mechanisms for the broadband wireless systems such as 3G and 3.5G. In order to reflect the underlying network conditions, they measure the bandwidth utilization and forecast the required bandwidth by applying a bandwidth estimation model (e.g., moving average or Gaussian estimation). Krithikaivasan et al. [8] proposed a sophisticated traffic forecasting and bandwidth provisioning method. A prediction algorithm derived from an auto-regressive integrated moving average (ARIMA) model has been developed for more accurate, dynamic bandwidth provisioning along with some positive results from performance evaluation using various data sets. However, this scheme does not take into account the heterogeneous types of traffic, and therefore, not directly applicable to the multi-class environment. It has been observed that service degradation approaches may increase bandwidth utilization and service provider’s revenue [10–12]. The common goal of the service degradation approaches is to increase bandwidth utilization by lowering the QoS levels of existing users. The work presented in [10] evaluated the effects of service degradation caused by adaptive bandwidth allocation. Although the system performance can be improved by allowing service degradation, the impact of degradation on the QoS of individual users should be considered. In this work, we attempt to find an adaptive bandwidth provisioning method without an assumption on statistical property of the traffic. Our approach consists of two stages: traffic forecasting, followed by bandwidth provisioning. For the first stage, we use ARIMA model to forecast traffic based on online measurement. For the second stage, we use a bandwidth provisioning scheme that allocates bandwidths depending on the traffic forecasting. We modeled our problem as a Fractional Knapsack Problem for which we used a greedy algorithm in order to find an approximate solution. The rest of the paper is organized as follows. An overview of the IEEE802.16 QoS class is summarized in Section 2. In Section 3, we present the overview of the ARIMA modeling of time series along with the identification of ARIMA models for two data sets used in our study. Next, we give an explanation on how to map the optimization problem to a Fractional Knapsack Problem. In Section 4, we evaluate the proposed dynamic bandwidth provisioning scheme with various data sets. Finally, in Section 5, conclusions follow.
2. The IEEE802.16 QoS traffic classes The bandwidth management scheme and its associated QoS parameters of the IEEE802.16 are defined in [1,2]. For media access control (MAC) layer QoS, the IEEE802.16 specifications define five QoS classes: UGS, rtPS, nrtPS, BE, and ertPS. The three main distinguishing factors among these classes are delay sensitivity, packet size fluctuation, and scheduling type. The UGS supports real-time service flows that generate fixed-size data packets on a periodic basis, whose typical example is constant bit rate (CBR) traffic such as voice-over-IP (VoIP) without silence suppression. The rtPS supports real-time service flows that generate variable-size data packets on a periodic basis, whose typical example is a variable bit rate (VBR) traffic such as moving pictures expert group (MPEG) video. The nrtPS supports nonreal-time service flows that require variable-size data packets on a regular basis. It is suitable for bulk data transfer such as high-bandwidth file transfer protocol (FTP). The BE
supports best effort traffic and suitable for bulk and asynchronous traffic flows such as the email. The ertPS supports real-time service flows that generate variable-size data packets on a periodic basis, as was the case for the rtPS, but it adopts the unsolicited method of bandwidth request, as was the case for the UGS. A typical example of service amenable to the ertPS is the VoIP service with silence suppression. Similarly, the Third-Generation Partnership Project (3GPP) and 3GPP2 define four QoS classes for wireless link: conversational, streaming, interactive, and background. The conversational class provides strict delay guarantees, while background class offers no qualitative or quantitative guarantees. It is the best effort class. The conversational and streaming classes are intended for realtime traffic such as voice and video applications. The interactive class is suitable for data transfer that has request–response patterns. These wireless QoS classes will be mapped to open Internet Engineering Task Force (IETF) QoS architectures (e.g., DiffServ and IntServ). For example, taking IEEE802.16 traffic class model and DiffServ framework into account, the expedited forwarding (EF) per-hop behavior (PHB) is a good candidate to be mapped to the UGS and ertPS classes. Examples of QoS mappings can be found in [13,14]. 3. Description of the proposed method This paper deals with appropriate QoS provisioning among four1 different QoS classes. The system under consideration is an integrated voice/data mobile network with real-time multimedia support. The Mobile WiMAX (especially, R6 interface) is the target environment that we used in our experiments. The main focus of our work is to apply the combination of ARIMA model and Fractional Knapsack Problem in QoS provisioning mechanism of WiMAX, which has not been proposed in the literature previously. Furthermore, we propose integration method of ARIMA and Fractional Knapsack Problem in alternating repetition. 3.1. Time series analysis using the ARIMA model Box and Jenkins [15] developed the ARIMA model which combined the AutoRegresive (AR) and Moving Average (MA) models developed earlier with a differencing factor that removes in trend in the data. A nonseasonal ARIMA model is classified as an ARIMA(p, d, q) model, where p is the number of auto-regressive terms, d is the number of nonseasonal differences, and q is the number of lagged forecast errors in the prediction equation. The Box–Jenkins methodology consists of the following three iterative steps. First, we determine whether the time series is stationary or nonstationary. If it is nonstationary, the series is represented by a new series by applying dth difference of the process to be stationary. Second, in order to identify the values of p and q, we examine the autocorrelation function (ACF) and partial autocorrelation function (PACF) of the time series. For the detailed introduction to model identification based on ACF and PACF, the reader is directed to [15]. Third, having determined p, d, and q, the coefficients of the AR and MA terms are estimated using a nonlinear least squares method. Let fX Ut j1 6 t 6 ng, fX Rt j1 6 t 6 ng, fX Nt j1 6 t 6 ng, and fX Bt j1 6 t 6 ng are the time series for which we want to predict their amount, where the subscripts U, R, N, and B stand for UGS, rtPS, nrtPS, and BE, respectively. In order to obtain the four time series, we monitor utilization of the bandwidth provisioned for each traffic class at a regular interval T. The time series of the link 1 We consider UGS, rtPS, nrtPS, and BE. We exclude ertPS for simplification purpose.
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utilization of UGS class, fX Ut g is expressed by previous observations X Utj , and noise term t which typically correspond to external events. The noise processes t are assumed to be uncorrelated with a zero mean and finite variance. The general ARIMA(p, d, q) model has the form
rd X Ut ¼
p X
Uj ðrd X Utj Þ þ t þ
i¼j
q X
t WNð0; r2 Þ:
hj tj ;
ð1Þ
j¼1
We use the concise form of this expression,
UðBÞrd X Ut ¼ hðBÞt ;
ð2Þ 2
p
where U(B) = 1 U1B U2B UpB is the auto-regressive operator of order p, h(B) = 1 h1B h2B2 hqBq is the moving average operator of q, rd = (1 B)d is the dth order difference operator, and B is the backward-shift operator, i.e., Bj X Ut ¼ X Utj ; Bj t ¼ tj . The same mathematical expression can be applied to fX Rt g, fX Nt g, and fX Bt g. We consider two different data sets downloaded from NLANR [16]. Each data set consists of 24-h data sampled at 6-min interval. We divide each data set into four different traffic classes based on the port numbers shown in Table 1. In order to determine the values of p, d, and q, we used the last 80 samples from each traffic class. First, we determine whether or not each sample data set is a stationary time series. Since they were all nonstationary, we obtained the first-order differences of actual time series X Ut , X Rt , X Nt , and X Bt to generate new times series, W Ut ¼ X Ut X Ut1 , W Rt ¼ X Rt X Rt1 , W Nt ¼ X Nt X Nt1 , and W Bt ¼ X Bt X Bt1 . These new time series were found to be stationary for all data sets, and therefore, we set d = 1 in our ARIMA model. Then, we examined the ACF and PACF plots to find the appropriate values of p and q. The mean square error tests indicated that the order of AR and MA components to be within [0, 4]. The values of p, d, and q can be subsequently updated using a set of samples including newly added measurement data. After identifying the model parameters, p, d, and q, we use the minimum mean square error (MMSE) forecast method to make a prediction. We simply use maximum likelihood point estimator to decide our forecast value. We denote the k-step-ahead predicb U . We call the k is the lead time. When k = 1, then we call tion as X tþk it is one-step-ahead prediction. The prediction performance is presented in Section 4. 3.2. Dynamic bandwidth provisioning using Fractional Knapsack Problem The Knapsack Problem has been widely used to model many resource sharing problems. In the standard Knapsack Problem, there is a set of items each with a value and a weight and a knapsack with a given fixed capacity. The objective is to determine the number of each item to include in a collection so that the total weight is less than a given limit and the total value is as large as possible. In the 0/1 Knapsack Problem each item must either be taken or left behind. However, in the Fractional Knapsack Problem each item can be subdivided. In our model, the weight and the value of the items can be regarded as the traffic amount of each class and traffic
Table 1 Traffic classification based on TCP/UDP port numbers. Class
UGS
rtPS
nrtPS
BE
Application
VoIP
FTP, file sharing
Email, Web
Port numbers
1863
Video/audio streaming 6660, 6661
20, 21, 53, 2122, 3830 6346, 6881, 9001, 9875
25, 80
priority, respectively. The capacity of knapsack corresponds to the total bandwidth. Detailed parameters mapping is shown in Table 2. Given a collection of traffic classes G = {g1, g2, . . . , gn}, where each traffic class gi = hvi, wii worth vi, and weight wi bps, our goal is to fill a wireless link with max-capacity of W bps with traffic classes from G, so that the total value of items in the link is maximized. It is allowed to take fraction of any item. Formally, given a filling pattern F = {f1, f2, . . . , fn} where 0 6 fi 6 1 denotes the fraction of the ith item P we take, the value of this pattern is V F ¼ ni¼1 fi v i and the weight of Pn this pattern is W F ¼ i¼1 fi wi . We wish to find a filling pattern F ¼ ff1 ; f2 ; . . . ; fn g such that W F 6 W, and V F is maximized. Let qi = vi/wi be the value per bps (VPB) for item-i, and sort the set of items by their VPB values. Assume that G = {g1, g2, . . . , gn} is such a sorted list. The Fractional Knapsack Problem can be solved by a greedy strategy as shown in following algorithm. Algorithm 1. Fractional_Knapsack (G, n, W) 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: 13:
/* G is already sorted by the VPB values of items. */ F is an array of size n, initialized to all zeros; Aw W; i 1; while Aw > 0 and i 6 n do if Aw P wi then fi 1; else fi Aw/wi; end if Aw Aw fiwi; i++; end while return F;
The output of the above algorithm, F, is an optimal solution. The proposed dynamic bandwidth provisioning scheme reprovisions bandwidth for each traffic class based on a forecasted bandwidth values as well as on the desired solution reflecting traffic priority of each class. The dynamic bandwidth provisioning algorithm is as follows: Algorithm 2. Dynamic Bandwidth Reprovisioning P bU þ X bR þ X bN þ X b B */ 1: /* Note that ni¼1 wi ¼ X tþ1 tþ1 tþ1 tþ1 Pn 2: if i¼1 wi < W then b U W=Pn wi ; 3: BW UGS X i¼1 tþ1 b R W=Pn wi ; 4: X BW nrPS i¼1 tþ1 b N W=Pn wi ; 5: X BW nrtPS i¼1 tþ1 b B W=Pn wi ; 6: X BW BE i¼1 tþ1 7: else 8: Fractional_Knapsack (G, n, W); /* returns F */ 9: /* i 2 G such that UGS, nrPS, nrtPS, BE. */ 10: while i 6 n do bi ; 11: BW i fi X tþ1
12: 13:
end while end if
When the link is underutilized, we provision the bandwidth for each traffic class proportional to the current traffic amount (lines 2–6). It helps in reducing packet drop probabilities of each class by increasing bandwidth to absorb traffic fluctuations. When the link has no room to accept data packets any more, the bandwidth for each class is reprovisioned according to Algorithm 1 to maximize the total value of items in the link. It can maximize the link utilization taking into account the revenue gain of an operator.
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Table 2 Parameters mapping for Fractional Knapsack Problem. Knapsack capacity
Total link bandwidth
Items Weight
Each service class (i.e., UGS, rtPS, nrtPS, BE) Expected traffic amount of each class (applying one-stepbR ; X bN ; X bB bU ; X ahead prediction) X
Value
Relative priority of each class (e.g., BE:nrtPS:rtPS:UGS = 1:2:3:4)
tþ1
tþ1
tþ1
tþ1
4. Experimental results and discussions In this section, performance of the proposed scheme is evaluated in terms of the packet drop ratio and bandwidth gain. We undertook a number of experiments with various data sets downloaded from NLANR [16] with different traffic sources, relative traffic priority, and sampling/action interval. We selected NLANR data sets since they have been widely accepted and used as generic Internet traffic traces. 4.1. ARIMA prediction with real traces We consider two different data sets collected April 23, 2006 (called, data set 1) and April 30, 2006 (called, data set 2), which are Global Positioning System (GPS)-synchronized IP header trace taken at the access link of the University of Auckland. Each data set consists of 24-h data sampled at a 6-min interval. We divide each data set into four different traffic classes based on the port numbers as shown in Table 1. We denote the ARIMA model with the parameters p, d, and q, as ARIMA(p, d, q). In order to determine the values of p, d, and q, we used the last 80 samples from each traffic class. As mentioned in Section 3, the first-order differences
of actual time series, W Ut ¼ X Ut X Ut1 , W Rt ¼ X Rt X Rt1 , W Nt ¼ X Nt X Nt1 , and W Bt ¼ X Bt X Bt1 were found to be stationary for all data sets, and therefore, we determined d = 1 in our ARIMA model. We examined the ACF and PACF plots to find the appropriate values of p and q. For the data set 1, the ACF plots for the last 80 samples indicated the order q of moving average component to be within [1,4] for all the traffic classes. However, the PACF plots suggested different possible orders for p, which turned out to be within [0, 4] for the UGS, nrtPS, and BE traffic classes and [1,3] for the rtPS traffic class. For the data set 2, the parameters p and q are within [1,4] for UGS, rtPS, and BE traffic and [0, 4] for nrtPS traffic class. Figs. 1 and 2 show the behavior of one-step ahead traffic forecast for data sets 1 and 2. The actual traffic values are shown as dotted lines; the corresponding predicted values are superimposed as solid lines. Fig. 3 shows total amount of bandwidth for the real traces (dotted lines) and its corresponding predicted values (solid lines). We assumed that the total link bandwidth is 22.2 Kb/s for data set 1 and 28.9 Kb/s for data set 2, respectively. Notice that the predicted values can capture the actual traffic values well for the four different traffic classes. Being a model based on past observations, the plots of ARIMA lags behind those of measured data. Notice that the predictions cannot follow rapid changes in traffic. Rapid changes tend to be faced often when the offered aggregate traffic load is low as in our two experiments (e.g., 22.2 and 28.9 Kb/s). Advanced forecasting algorithms such as [17,18] may help in these undesirable instants.
4.2. Bandwidth reprovisioning Our goal is to compare the performance of the proposed scheme to the two conventional schemes, static and semi-static provision-
Fig. 1. Observed traffic amount and predictions with the data set measured in April 23, 2006. (a) UGS class, (b) rtPS class, (c) nrtPS class, and (d) BE class.
H.-W. Kim et al. / Computer Communications 34 (2011) 99–106
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Fig. 2. Observed traffic amount and predictions with the data set measured in April 30, 2006. (a) UGS class, (b) rtPS class, (c) nrtPS class, and (d) BE class.
Fig. 3. Observed total traffic amount and predictions. (a) Data set measured in April 23, 2006 and (b) data set measured in April 30, 2006.
ing. In the static provisioning, bandwidth for each traffic class is provisioned statically based on the average traffic amount for each class. Initially we provisioned 0.105 Kb/s for UGS, 15.1 Kb/s for rtPS, 4.9 Kb/s for nrtPS, and 2.1 Kb/s for BE class for data set 1 and 0.113 Kb/s for UGS, 13.5 Kb/s for rtPS, 13.2 Kb/s for nrtPS, and 2.1 Kb/s for BE class for data set 2. In fact, these values are not typical WiMAX data rates, since they are derived from the given data set. In the semi-static provisioning, bandwidth for each traffic class is provisioned statically, but with the priority of each class taken into account. We assume that the relative priority is 1:2:3:4 for BE, nrtPS, rtPS, and UGS class. The experiments were performed over a period of 16 h. The first experiment with data set 1 was performed with the following parameters: the p, d, q values determined in the previous subsection, the sampling interval T = 6 m, the number of samples, n = 80, the reprovisioning interval 6 m, and Fractional Knapsack parameters described in Table 2. The second experiment with data
set 2 was performed with the same parameters as the first experiment except using different p, d, q values. The bandwidth for each of the four traffic classes is reprovisioned according to the proposed scheme (i.e., Algorithm 2), which is based on the predicted bandwidth amount of each class and Fractional Knapsack Problem. We found the appropriate solution for packing the four classes into the given link. The various choices of vi chosen here are: hvBE, vnrtPS, vrtPS, vUGSsi = h1, 1, 1, 1i and h1, 2, 3, 4i. 4.2.1. Packet drops Fig. 4(a) and (b) shows the total packet drop probabilities for the proposed scheme, static provisioning, and semi-static provisioning. For all the schemes, the number of packet drops depends on the offered traffic load. In static provisioning for data set 1, the data loss of 0.673 MB in average was monitored between t = 0 and t = 16 and 0.671 MB in semi-static provisioning. When the proposed reprovisioning scheme was used for data set 1, the
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Fig. 4. Total packet drop probabilities. (a) Data set measured in April 23, 2006 and (b) data set measured in April 30, 2006.
data loss of 0.602 MB in average was observed between t = 0 and t = 16. For data set 2, we observed the data loss of 1.3 MB, 1.15 MB, 0.89 MB in average for static, semi-static, and the proposed scheme, respectively. In most cases, the packet drop probabilities of the proposed scheme is smaller than the two conventional schemes, static and semi-static provisioning. It is evident that even for two different set of vi values (i.e., h1, 1, 1, 1i and h1, 2, 3, 4i), the total amount of the packet drops are the same. Recall that vi values only affect relative ratio of the packet drop probabilities among four different traffic classes. Note that our prediction-based approach shows quite significant packet drop rate as high as 20% for some time intervals. It is due to the experimental conditions of quite low total link bandwidths (i.e., 8 Mb/s for data set 1 and 10.4 Mb/s for data set 2) and relatively heavy offered load as shown in Fig. 3. Although BE traffic suffers most in both vi = h1, 1, 1, 1i or vi = h1, 2, 3, 4i, the gain obtained from saving higher priority traffic enhances the total value of items in the link. In order to have a direct observation on the different treatments on different traffic classes, we show the individual packet drop
probabilities of each traffic class. Fig. 5(a) and (b) presents the packet drop probabilities for the proposed scheme (with two different vi-value sets), static provisioning, and semi-static provisioning. In Fig. 5(a), we observe an average loss of nearly 11.13% for BE, 9.66% for nrtPS, 0% for rtPS, and 19.01% for UGS when static provisioning scheme is used. We observe different packet loss behavior for semi-static provisioning scheme: 15.86% for BE, 2.24% for nrtPS, 5.41% for rtPS, and 3.63% for UGS. The reason why UGS has low loss ratio is that semi-static provisioning scheme provisions bandwidth statically, but takes relative traffic priorities into account. Note that each bar in the graphs shows the probabilities, not absolute value of the lost packets or bytes. Because we initially provisioned relatively small amount for UGS (0.105 Kb/s) and BE (2.1 Kb/s) compared to rtPS (15.1 Kb/s) and nrtPS (4.9 Kb/s), the significant increase or decrease of the loss probabilities of BE and UGS does not imply noticeable increase or decrease of lost packets or bytes. When we look at the loss ratio behavior for the proposed scheme with vi = h1, 1, 1, 1i, we observe that drop probabilities are better compared to static provisioning. On the other hand, the drop
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Fig. 5. Packet drop probabilities per class. (a) Data set measured in April 23, 2006 and (b) data set measured in April 30, 2006.
probability of nrtPS (5.52%) is worse compared to semi-static provisioning while the drop probabilities of BE (8.91%) and rtPS (0.33%) are better compared to static provisioning. We recall here that the total loss ratio from the proposed scheme mostly lies below that of static and semi-static provisioning scheme as shown in Fig. 4(a) and (b). Because we initially provisioned very small amount for UGS (0.105 Kb/s) compared to rtPS (15.1 Kb/s), nrtPS (4.9 Kb/s), and BE (2.1 Kb/s), the increased amount in the average loss ratio for UGS is actually quite small amount in terms of number of packets. By choosing vi = h1, 2, 3, 4i, we observe that almost the same drop probabilities of UGS and rtPS with vi = h1, 1, 1, 1i case. However, the drop probability of nrtPS decreases to 2.38% while drop probability of BE increases to 18.12%. It is due to the different filling pattern F, which is derived by Algorithm 1. We observe a similar behavior with data set 2 as shown in Fig. 5(b). High BE packet drops may cause many retransmissions and lead to TCP congestion control (e.g., slow start). The overall throughput for BE class may decrease, but high packet drop rate for BE class will not sustain. 4.2.2. QoS Satisfaction Index The bandwidth gain is an important measure because it has implications not only for reducing the call blocking probability of the high priority traffic classes but also increasing resource utilization. Since each class has a different priority, the simple bandwidth gain is not an appropriate indication of network resource utiliza-
tion gain. In order to represent the bandwidth gain, we define QoS Satisfaction Index (QSI). It is supplementary information. Let pj(t) denote the packet drop probability of traffic class j at time t where j = 1 for BE, j = 2 for nrtPS, j = 3 for rtPS, and j = 4 for UGS class. The QSI at time t can be expressed as
P4 QSIðtÞ ¼
j¼1 X j ðtÞð1 pj ðtÞÞzj P4 j¼1 X j ðtÞ
;
ð3Þ
where Xj(t) is traffic amount for class j measured at time t and zj is P relative priority among traffic classes and all j zj ¼ 100. Fig. 6(a) and (b) shows the QSI(t) plots for data sets 1 and 2 with vi = h1, 1, 1, 1i and vi = h1, 2, 3, 4i, respectively. As shown in Fig. 6, the QSI(t) plots tend to be in inverse proportion to number of packet drops. Note that the QSI value of the proposed scheme remains high when the offered load is high, but the static and semi-static provisioning schemes show a slight fall as the load increases. As shown in Fig. 6(a), in static provisioning for data set 1, the QSI value is average 94.9% between t = 0 and t = 16 and average 95.1% in semi-static provisioning. Although the amount of data loss is similar in the static and semi-static provisioning (i.e., 0.673 MB for static and 0.671 MB for semi-static), the QSI values show some difference. The reason why semi-static has better performance in terms of QSI is that the high priority traffic such as UGS and rtPS class experienced low data loss. When the proposed reprovisioning scheme is adopted for data set 1, average 96.8% (with vi = h1, 1, 1, 1i)
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low priority class as well. The bandwidth of each traffic class is predicted through ARIMA(p, d, q) model and the bandwidth reprovisioning problem is modeled as a Fractional Knapsack Problem for which we used a greedy algorithm (Algorithms 1 and 2) in order to find an approximate solution. The experiments performed using real link traces showed that the proposed reprovisioning scheme enables the total number of packet drops to be reduced and QoS Satisfaction Index (QSI) to be increased. As shown in our experimental results, while our approach works quite well most of the time, it is not perfect. The difficulties remain whenever an extremely unexpected turn in traffic is faced. The reprovisioned bandwidth for each traffic class can be used as an essential input to a CAC entity in Mobile WiMAX system. For example, a CAC entity may accept or deny a new VoIP call request based on the reprovisioned UGS bandwidth. Acknowledgments This work was supported in part by the IT R&D program of MKE/ KEIT [KI002084, A Study on Mobile Communication System for Next-Generation Vehicles with Internal Antenna Array] and the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (No. 2010-0027805). References
Fig. 6. QoS Satisfaction Index. (a) Data set measured in April 23, 2006 and (b) data set measured in April 30, 2006.
and 97.0% (with vi = h1, 2, 3, 4i) QSI were observed between t = 0 and t = 16. For data set 2, we observed average 90.8%, 91.9%, 95.6%, and 96.3% QSI in static, semi-static, the proposed scheme with vi = h1, 1, 1, 1i, and with vi = h1, 2, 3, 4i respectively. In summary, the QSI of the proposed scheme is better than the two conventional schemes, static and semi-static provisioning. Although at a specific time interval, static and semi-static provisioning scheme seems to perform well, but in average, the proposed scheme shows a better performance. 5. Conclusions The Mobile WiMAX is expected to support diverse real-time applications such as videoconferencing, voice-over-IP, and online gaming, demanding different QoS and bandwidth. Bandwidths for Mobile WiMAX system need to be properly provisioned for efficient use of the limited network resources. Releasing unutilized bandwidth for use by other services is important for increasing resource utilization. We have investigated how to increase the available bandwidth for high priority class (e.g., UGS) traffic while guaranteeing adequate service quality for
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