Cost- and Energy-Aware Multi-Flow Mobile Data Offloading Using Markov Decision Process

01/30/2018 ∙ by Cheng Zhang, et al. ∙ 0

With the rapid increase in demand for mobile data, mobile network operators are trying to expand wireless network capacity by deploying wireless local area network (LAN) hotspots on which they can offload their mobile traffic. However, these network-centric methods usually do not fulfill the interests of mobile users (MUs). Taking into consideration many issues, MUs should be able to decide whether to offload their traffic to a complementary wireless LAN. Our previous work studied single-flow wireless LAN offloading from a MU's perspective by considering delay-tolerance of traffic, monetary cost and energy consumption. In this paper, we study the multi-flow mobile data offloading problem from a MU's perspective in which a MU has multiple applications to download data simultaneously from remote servers, and different applications' data have different deadlines. We formulate the wireless LAN offloading problem as a finite-horizon discrete-time Markov decision process (MDP) and establish an optimal policy by a dynamic programming based algorithm. Since the time complexity of the dynamic programming based offloading algorithm is still high, we propose a low time complexity heuristic offloading algorithm with performance sacrifice. Extensive simulations are conducted to validate our proposed offloading algorithms.

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1 Introduction

The mobile data traffic demand is growing rapidly. According to the investigation of Cisco Systems [1], the mobile data traffic is expected to reach 24.3 exabytes per month by 2019, while it was only 2.5 exabytes per month at the end of 2014. On the other hand, the growth rate of the mobile network capacity is far from satisfying that kind of the demand, which has become a major problem for wireless mobile network operators (MNOs). Even though 5G technology is promising for providing huge wireless network capacity [2], the development process is long and the cost is high. Economic methods such as time-dependent pricing [3][4] have been proposed to change users’ usage pattern, which are not user-friendly. Up to now, the best practice for increasing mobile network capacity is to deploy complementary networks (such as wireless LAN and femtocells), which can be quickly deployed and are cost-efficient. Using such methods, part of the MUs’ traffic demand can be offloaded from a MNO’s cellular network to the complementary network.
The process that a mobile device automatically changes its connection type (such as from cellular network to wireless LAN) is called vertical handover [5]. Mobile data offloading is facilitated by new standards such as Hotspot 2.0 [6] and the 3GPP Access Network Discovery and Selection Function (ANDSF) standard [7], with which information of network (such as price and network load) can be broadcasted to MUs in real-time. Then MUs can make offloading decisions intelligently based on the real-time network information.
There are many works related to the wireless LAN offloading problem. However, previous works either considered the wireless LAN offloading problem from the network providers’ perspective without considering the MU’s quality of service (QoS) [8][9], or studied wireless LAN offloading from the MU’s perspective [10][11] [12][13], but without taking the energy consumption as well as cost problems into consideration.
Our previous work [14] studied the wireless LAN offloading problem from the MU’s perspective. The MU’s target was to minimize its total cost, while taking monetary cost, preference for energy consumption, availability of MU’s mobility pattern and application’s delay tolerance into consideration. A Markov decision process algorithm [15][16][17]

was proposed for a known MU’s mobility pattern case and a reinforcement learning

[18] based algorithm was proposed for an unknown MU’s mobility pattern case. However, [14] only considered a MU’s single flow. Actually, a MU always execute mulitple applications simultaneously with modern mobile devices that have powerful multi-task abilities. Therefore, multi-flow mobile data offloading problem from a MU’s perspective is more relevant and remains to be solved.
In this paper, we study the wireless LAN offloading problem from a MU’s perspective considering multi-flow. Each flow has different delay tolerance. The MU’s target is to minimize its total cost, which includes the monetary cost and energy consumption cost, while taking the MNO’s usage base price, the MU’s preference for energy consumption, and flows’ delay tolerance into consideration. The cost- and energy-aware wireless LAN offloading problem is modeled as a finite-horizon discrete-time Markov decision process (FDTMDP) under the assumption that the MU’s mobility pattern is known in advance. We propose a dynamic programming based algorithm to solve the FDTMDP problem. However, the time complexity of the dynamic programming based offloading algorithm is high. Therefore, we propose a heuristic offloading algorithm with low time complexity and performance sacrifice. We conduct the simulations to verify the performance of the proposed schemes, and the simulation results show that the dynamic programming based offloading algorithm can minimize the MU’s monetary cost and save energy of the MU’s device, while the heuristic offloading algorithm has comparable performance in terms of cost minimization and energy saving for the MU.
The proposed mobile data offloading algorithms can be implemented on the MUs’ device without modification of the network system. The MUs themselves, or third-party application developers can utilize our work to save monetary cost and energy for the MUs.
The rest of this paper is organized as follows. Section 2 describes the related work. Section 3 illustrates the system model. Section 4 formulates the user’s wireless LAN offloading problem as discrete-time finite-horizon Markov decision process and proposes a dynamic programming based algorithm. Section 5 proposes a low time complexity heuristic offloading algorithm. Section 6 illustrates the simulation and results. Finally, we conclude this paper in Section 7.

2 Related Work

Mobile data offloading has been widely studied in the past. Gao et al. [8] studied the cooperation among one MNO and multiple access point owners (APOs) by utilizing the Nash bargaining theory, and the case of multiple MNOs and multiple APOs is studied in [9], where double auctions were adopted. The aforementioned papers [8][9] considered the mobile data offloading market from the perspective of the network without considering the MU’s experience directly.
On the other hand, papers[10][11][12][13] have considered offloading delay-tolerant traffic from the MUs’ perspective. In [10], Balasubramanian et al. implemented a prototype system called Wiffler to leverage delay-tolerant traffic and fast switching to 3G. Im et al. [12]

not only took a MU’s throughput-delay tradeoffs into account, but also considered the MU’s 3G budget explicitly. A MU’s mobility pattern was predicted by a second-order Markov chain. In

[13], Cheung studied the problem of offloading delay-tolerant applications for each user. A Markov decision process was formulated to minimize total data usage payment. Similar to [13], Kim et al. in [19] also utilized a Markov decision process based approach to allocate cellular network or wireless LAN data rate to maximize a MU’s satisfaction, which only depended on the MU’s wireless LAN usage.
The above literature does not consider the energy consumption problem when offloading traffic from a cellular network to a complementary network. Actually, the battery life has always been a concern for smartphones. [20][21] have studied how to design an energy-efficient framework for mobile data offloading. However, the trade off between throughput, delay and budget constraints have not been considered in these works. While it was shown in [11] that wireless LAN data offloading saved 55% of battery power due to the much higher data rate wireless LAN can provide, it was verified in [21] that wireless LAN could consume more energy than cellular network when wireless LAN throughput was lower. In order to clarify the contradiction, it is necessary to consider energy consumption to establish a cost- and energy-aware mobile data offloading scheme.
Our previous work [14] studied the wireless LAN offloading problem from a MU’s perspective. The MU’s target was to minimize its total cost under usage based pricing, while taking monetary cost, preference for energy consumption, availability of the MU’s mobility pattern and application’s delay tolerance into consideration. A Markov decision process algorithm was proposed for a known MU’s mobility pattern case and a reinforcement learning [18] based algorithm was proposed for an unknown MU’s mobility pattern case. However, [14] only considered a MU’s single flow case.
Different from the aforementioned papers, in this paper, we study a multi-flow mobile data offloading problem in which a MU has multiple applications to transmit data simultaneously with different deadlines, as well as considering the MU’s monetary cost and energy consumption.

Fig. 1: System scenario.

3 System Model

Since the cellular network coverage is rather high, it is assumed that the MU is always in a cellular network, but not always can access wireless LAN access points (APs). The wireless LAN APs are usually deployed at home, stations, shopping malls and so on. Therefore, we assume that wireless LAN access is location-dependent (see Fig. 1). We mainly focus on applications with data of relative large size and delay-tolerance to download, for example, applications like software updates, file downloads, or emails with attachments. The MU has files to download from a remote server. Each file formulates a flow, and the set of flows is denoted as . Each flow has a deadline . T

is the deadline vector for the MU’s

flows. Please note that we only consider downlink communication in this paper. Without loss of generality, it is assumed that . We consider a slotted time system as . To simplify the analysis, we use limited discrete locations instead of infinite continous locations. It is assumed that a MU can move in possible locations, which is denoted as set . While the cellular network is available at all the locations, the availability of wireless LAN network is dependent on location . The MU has to make a decision on what network to select and how to allocate the available data rate among flows at location at time by considering total monetary cost, energy consumption and remaining time for data transmission. A MU’s mobility can be modelled by a Markovian model as in [12][13]. Therefore, the MU’s decision making problem can be modelled as a finite-horizon Markov decision process.

Fig. 2: An example of MDP modelling: at time , the state 1 contains location and remaining file size B. MU chooses actions of Wireless LAN, Cellular network, or Idle, which incur different cost on MU. The fraction number under the action

is the transition probability which depends on MU’s mobility pattern. The objective of MU is to minimize total cost from time

to (cost 1 + cost 2 + … + cost T).

We define the system state at as in Eq. (1)

(1)

where is the MU’s location index at time , which can be obtained from GPS. is the location set. is the vector of remaining file sizes of all flows at time , for all . is the total remaining data size for flow . =, is the set vector of remaining data.
The MU’s action

at each decision epoch

is to determine whether to transmit data through wireless LAN (if wireless LAN is available), or cellular network, or just keep idle and how to allocate the network data rate to flows. Therefore, the MU’s action vector is denoted as in Eq. (2)

(2)

where denotes the vector of cellular network allocated data rates, denotes the cellular data rate allocated to flow , and denotes the vector of wireless LAN network allocated data rates, and denotes the wireless LAN rate allocated to flow . Here the subscript and stand for cellular network and wireless LAN, respectively. Please note that , , …, all can be 0 if the MU is not in the coverage area of wireless LAN AP. Even though it is technically possible that wireless LAN and cellular network can be used at the same time, we assume that the MU can not use wireless LAN and cellular network at the same time. We make this assumption for two reasons: (i) If we restrict the MU to use only one network interface at the same time slot, then the MU’s device may be used for longer time for the same amount of left battery. (ii) Nowadays smartphones, such as an iPhone, can only use one network interface at the same time. We can easily implement our algorithms on a MU’s device without changing the hardware or OS of the smartphone if we have this assumption. At time , MU may choose to use wireless LAN (if wireless LAN is available) or cellular network, or not to use any network. If the MU chooses wireless LAN at , the wireless LAN network allocated data rate to flow , , is greater than 0, and the MU does not use cellular network in this case, then = 0. On the other hand, if the MU chooses cellular network at , the cellular network allocated data rate to flow , , is greater than 0, and the MU does not use wireless LAN in this case, then = 0. , should not be greater than the remaining file size for flow .
The sum data rate of all the flows of cellular network and wireless LAN are denoted as and , respectively. and should satisfy the following conditions.

(3)
(4)

and are the maximum data rates of cellular network and wireless LAN, respectively, at each location .

Notation Description
, MU’s flows set.
T T, MU’s deadline vector.
, the specific decision epoch of MU.
, the location set of MU.
, the total size of MU’s flow. .
, vector of remaining file size.
, state of MU.
, MU’s location index at time .
cellular data rate allocated to flow at time
wireless LAN data rate allocated to flow at time
cellular throughput in bps at location .
wireless LAN throughput in bps at location .
energy consumption rate of celllar network in joule/bits at location .
energy consumption rate of wireless LAN in joule/bits at location .
energy preference of MU at .
MNO’s usage-based price for cellular network service.
MU’s penalty function for remaining data at .
MU’s energy consumption at .
, transmission decision at .
, MU’s policy.

TABLE I: Notations summary.

At each epoch , three factors affect the MU’s decision.

  • (1) the monetary cost: it is the payment from the MU to the network service provider. We assume that the network service provider adopts usage-based pricing, which is being widely used by carriers in Japan, USA, etc. The MNO’s price is denoted as . It is assumed that wireless LAN is free of charge. We define the monetary cost as in Eq. (5)

    (5)
  • (2) the energy consumption: it is the energy consumed when transmitting data through wireless LAN or cellular network. We denote the MU’s awareness of energy as in Eq. (6)

    (6)

    where is the energy consumption rate of the cellular network in joule/bits at location and is the energy consumption rate of the wireless LAN in joule/bits at location . It has been shown in [21] that both and decrease with throughput, which means that low transmission speed consumes more energy when transmitting the same amount of data. According to [22], the energy consumptions for downlink and uplink are different. Therefore, the energy consumption parameters and should be differentiated for downlink or uplink, respectively. In this paper, we do not differentiate the parameters for downlink or uplink because only the downlink case is considered. Nevertheless, our proposed algorithms are also applicable for uplink scenarios with energy consumption parameters for uplink. is the MU’s preference for energy consumption at time . is the weight on energy consumption set by the MU. Small means that the MU cares less on energy consumption. For example, if the MU can soon charge his smartphone, he may set to a small value, or if the MU is in an urgent status and could not charge within a short time, he may set a large value for . = 0 means that the MU does not consider energy consumption at all in the process of data offloading, just like in [13] [19].

  • (3) the penalty: if the data transmission does not finish in deadline , , the penalty for the MU is defined as Eq. (7).

    (7)

    where is a non-negative non-decreasing function. means that the penalty is calculated after deadline .

The probabilities associated with different state changes are called transition probabilities. We denote transition probability as in Eq. (8)

(8)

Eq. (8) shows the probability of state if action is chosen at state . It is assumed that the remaining size is independent of location change, therefore

(9)

where

(10)

is equal to . The MU’s probability from to is denoted as , which is assumed as known (see Assumption 1).

Assumption 1

The MU’s mobile probability to move from the current location to the next location is known in advance.

The MU’s mobility pattern can be derived from the MU’s historical data, which has been widely studied in the literature, such as [12].
The MU’s policy is defined as in Eq. (11)

(11)

where is a function mapping from state to a decision action at . The set of is denoted as . If policy is adopted, the state is denoted as .
The objective of the MU is to the minimize the expected total cost (include the monetary cost and the energy consumption) from to and penalty at with an a optimal (see Eq. (12))

(12)

where is the sum of the monetary cost and the energy consumption as in Eq. (13)

(13)

Please note that the optimal action at each does not lead to the optimal solution for the problem in Eq. (12). At each time , not only the cost for the current time should be considered, but also the future expected cost.
Please refer to Fig. 2 for an example of a MDP modelling in this section. The notations used throughout this paper are summarized as shown in Table 1.

4 Dynamic Programming Based Algorithm

The MU’s network selection and rate allocation problem has been formulated as a standard finite-horizon discrete-time Markov decision process (MDP). The target of the MU is to choose a set of actions to minimize his cost as shown in Eq. (12). In this section, we propose a dynamic programming based algorithm to solve the problem in Eq. (12).
For a MDP problem, it is important to identify the optimality equation (or Bellman equation) [23]. Denote as the minimal expected total cost of the MU from to at state . The Bellman equation is defined as in Eq. (14).

(14)

where for , , we have

(15)

Based on the Bellman equation Eq. (14), we propose Algorithm 1. In the optimal policy calculation phase, the optimal policy is calculated by backward induction from epoch to 1, where is the granularity of the total data size . Then, the MU’s offloading data policy is decided in each slot in the offloading data transmission phase. It is obvious that the time complexity of Algorithm 1 is .

Theorem 1

The policy generated in Algorithm 1 is the problem (12)’s optimal solution.

Proof: It is obvious according to the principle of optimality defined in [23].

Q.E.D

Algorithm 1: Dynamic Programming Based Algorithm
1: Optimal Policy Calculation Phase
2: Set , , by Eq. (7)
3: Set :=
4: while :
5:    for :
6:       Set =0
7:       for :
8:          Calculate using Eq. (14)
9:          Set :=
10:          Set :=
11:          Set :=
12:       end for
13:    end for
14:    Set :=
15: end while
16: The optimal policy is generated for the following offloading data transmission phase
17:
18: Offloading Data Transmission Phase
19: Set ,
20: while and :
21:     is determined from GPS
22:    Set action according to (the optimal policy)
25:       Set
26:    end if
27:    Set
28: end while

5 Low Time Complexity Heuristic Offloading Algorithm

A dynamic programming based mobile offloading algorithm (Algorithm 1) has been proposed in Sect. 4, and Theorem 1 guarantees the optimality of this algorithm. However, time complexity of Algorithm 1 is rather high. Furthermore, the Optimal Policy Calculation Phase of Algorithm 1 should be performed in advance, which means that Algorithm 1 is an offline algorithm. Therefore, two questions may arrise.

  • Is there a low time complexity algorithm solution for the MU’s problem in Eq. (12)?

  • How to generate the MU’s policy in a real-time manner without calculations in advance as in Algorithm 1?

Algorithm 2: Low Time Complexity Heuristic Offloading Algorithm
1: At time slot
2: Input: T, , ,
3: for T:
4:    if :
5:       Add to deadline remain list R
6:       Set =
7:    else:
8:       Set
9:    Add to rate allocation weight list
10:    end if
11: end for
13: Normalize to
13: Normalize to
12: =multiply() //multiply by element
13: Normalize to
14: if wireless LAN access is available at location and speed is greater than :
15:    Allocate wireless LAN data rate to each flow according to weight list .
16:        is determined
17: else if :
18:    Allocate cellular data rate to each flow according to weight list .
19:        is determined
20: end if
21: Output: )

In this section, we try to answer the aforementioned two questions and thus avoid the problems posed by the dynamic programming based Algorithm 1 in Sect. 4. An online low time complexity heuristic offloading algorithm is proposed as shown in Algorithm 2 by the following arguments:

  • (i) a flow with a earlier deadline should have a higher priority;

  • (ii) the more remaining file size, the higher is the priority of the flow;

  • (iii) the wireless LAN network should have a priority since it has a lower price than the cellular network;

  • (iv) when the flow deadline is approaching, the cellular network should also be used to try to finish the data transmission, without waiting for access to a wireless LAN network;

  • (v) a low speed wireless LAN network, which consumes a lot of energy for data transmission, should be ignored to save energy if the MU concerns about the energy consumption;

We briefly explain Algorithm 2 below.

The main task is to first calculate the allocation weight W, then allocate the wireless LAN data rate or cellular data rate based on the calculated allocation weight. The inputs of the algorithm are deadline vector T, deadline threshold (which will be explained later), location , and remaining file size vector b. The flow with the least remaining deadline has the highest priority, which is calculated as weight = . Here is the deadline for flow . is the weight list for deadlines, which reflects the aforementioned rationale (i). Considering argument (ii) above, the weight list for deadlines should be multiplied by the remaining file size vector after normalization ( is the normalization of and is the normalization of ). The result of multiplication is denoted as W. The reason why normalization is necessary is that the weight for a deadline and the remaining file size are of different scales. While wireless LAN has the priority, we have to use wireless LAN when possible. However, if the speed of a wireless LAN is lower than a threshold , the wireless LAN should not be used because it is energy-consuming (rationale (v)). Please note that is a parameter that is determined by the MU’s energy preference . If the MU is concerned about energy consumption (high ), the MU will eliminate low speed APs by setting a high threshold . If there is no wireless LAN, the MU has to wait for wireless LAN without using cellular network. Yet if the least remaining time for data transmission is less than threshold , the cellular network also should be selected for data transmission (rationale (iv)).
It is obvious that the time complexity of Algorithm 2 is , which is much lower than that of Algorithm 1 and there is no offline calculation phase for Algorithm 2, therefore, the decision is made in an online manner.

6 Performance Evaluation

In this section, the performances of our dynamic programming based algorithm (Proposed DP) and heuristic offloading (Proposed Heuristic) algorithm are evaluated by comparing them with a Baseline algorithm that use wireless LAN AP to offload traffic whenever possible and the algorithm called DAWN in [13]. We developed a simulator with Python 2.7, which can be downloaded from the following URL link: https://github.com/aqian2006/OffloadingMDP.
A four by four grid is used in simulation. Therefore, is 16. Wireless LAN APs are randomly deployed in locations. The cellular usage price is assumed as 1.5 yen/Mbyte. means that the probability that the MU stays in the same place from time to is 0.6. And the MU moves to the neighbour location with equal probability, which can be calculated as . The average Wireless LAN throughput is assumed as 15 Mbps111We tested repeatedly with an iPhone 5s on the public wireless LAN APs of one of the biggest Japanese wireless carriers. The average throughput was 15 Mbps. , while average cellular network throughput is 10 Mbps222We also tested with an iPhone 5s on one of the biggest Japanese wireless carriers’ cellular network. We use the value 10 Mbps for average cellular throughput.

. We generate wireless LAN throughput for each AP from a truncated normal distribution, and the mean and standard deviation are assumed as 15Mbps and 6Mbps respectively. The wireless LAN throughput is in the range [9Mbps, 21Mbps]. Similarly, we generate cellular throughput from a truncated normal distribution, and the mean and standard deviation are assumed as 10Mbps and 5Mbps respectively. The cellular network throughput is in range [5Mbps, 15Mbps].

in Algorithm 1 is assumed as 1 Mbits. Time for each epoch is 1 seconds. The penalty function is assumed as =. Please refer to Table III for the parameters used in the simulation.

Fig. 3: Energy consumption (joule/Mb) vs. Throughput (Mbps).
Throughput (Mbps) Energy (joule/Mb)
11.257 0.7107
16.529 0.484
21.433 0.3733
TABLE II: Energy vs. Throughput.

Because the energy consumption rate is a decreasing function of throughput, we have the sample data from [24] (see Table II). We then fit the sample data by a exponential function as shown in Fig. 3. We also made a new energy-throughput function as , which is just lower than . We basically use if we do not explicitly point out. Please note that the energy consumption rate of cellular and wireless LAN may be different for the same throughput, but we assume they are the same and use the same fitting function as in Fig. 3.

Parameters Value
16
B Mbits
Number of wireless LAN APs 8
1 Mbits
time slot 1 seconds
average of 10 Mbps
standard deviation of 5 Mpbs
average of 15 Mbps
standard deviation of 6 Mpbs
0.6
(1-0.6)/#neigbour locations
1.5 yen per Mbyte
=
TABLE III: Parameters in the simulation.
Fig. 4: Energy consumption (joule) vs. MU’s energy preference ().

In Fig.4, our proposed DP and heuristic algorithms are compared to the DAWN algorithm in [13] in terms of the MU’s energy consumption. Since [13] only considered a single-flow case, we also apply our algorithms to a single-flow. It is shown that the larger the MU’s energy preference, the lower the energy consumed for our MDP and heuristic algorithms. The energy consumption of the DAWN algorithm is higher than that of our algorithm. The heuristic algorithm is not optimal, but it is close to the optimal result of proposed DP algorithm. The reasons is that energy consumption was not considered in the DAWN algorithm, while our proposed DP and heuristic algorithms have taken energy consumption into consideration and tried to minimize total energy consumption.

Fig. 5: Monetary cost (yen) vs. No. of flows.
Fig. 6: Energy consumption (joule) vs. No. of flows with different energy-throughput functions and .

Fig.5 and shows the comparison of monetary cost among Baseline, Proposed Heuristic, and Proposed DP algorithms with different number of flows. The monetary cost of all three algorithms increases with the number of flows. The monetary cost of Proposed DP is lower than Baseline, while Proposed Heuristic is close to Proposed DP. The reason is that in Baseline, data are downloaded whenever there is a network (cellular or wireless LAN) available, without considering the monetary cost by using the cellular network. In Proposed DP and Proposed Heuristic, whether the cellular network is used depends on the remaining data to download and the deadline. If there are only relatively few remaining data and enough time left until the deadline, our proposed algorithms will choose to wait for a cheap wireless LAN to download data.

Fig.6 shows the comparison of the energy consumption among Baseline, Proposed Heuristic, and Proposed DP algorithms with different number of flows. Two energy-throughput functions and are used. The performance of Proposed DP algorithm is the best, but the Proposed Heuristic algorithm shows small differences with that of Proposed DP algorithm with either or . For Proposed DP/Proposed Heuristic/Baseline, the energy consumption under is much higher than that under . The reason is that the energy consumption for a certain throughput is higher under than that under . Our Proposed DP algorithm consumes the least energy since we attempt to minimize the total energy consumption by formulating a MDP problem.

Fig. 7: Monetary cost (yen) vs. No. of APs.
Fig. 8: Energy consumption (joule) vs. No. of APs with different energy-throughput functions and .
Fig. 9: Finish rate vs. No. of APs.

Fig.7 shows the comparison of monetary cost among Baseline, Proposed Heuristic, and Proposed DP algorithms with different number of APs. It can be seen that the monetary cost of Proposed DP algorithm is lowest, and the baseline algorithm is highest. While the monetary cost of the Proposed Hueristic algorithm is between that of Baseline, it is much closer to the Proposed DP algorithm. With a large number of wireless LAN APs deployed, the chance of using cheap wireless LAN increases. Therefore, the MU can reduce his monetary cost by using cheap wireless LAN. Therefore, all three algorithms’ monetary costs decreases with the number of APs.
Fig.8 shows how the MU’s energy consumption changes with the number of deployed APs under the two energy-throughput functions and . Similar to Fig.6, the performance of Proposed DP algorithm is the best with either or . It shows that the energy consumptions of all three algorithms just slightly decrease with the number of APs. The reason is that the energy consumption depends on the throughput. The larger the throughput, the lower is the energy consumption. With large number of wireless LAN APs, the MU has more chance to use wireless LAN with high throughput since the average throughput of a wireless LAN is assumed as higher than that of cellular network (see Table III).
Fig.9 shows the finish rate comparison among Basedline, Proposed DP and the Proposed Heuristic algorithm with different number of wireless LAN APs. Here, finish rate is defined as the ratio of the number of flows with finished transmission to the total number of flows started. Even though there are penalties for flows’ remaining data, not all the flows can be finished before their deadlines. Finish rate of Proposed DP and the Proposed Heuristic algorithms increases with the number of wireless LAN APs deployed. The reason is that a large number of cheap and high throughput wireless LAN APs decreases the overall download time.

There are two limitations for our proposed DP and heuristic algorithms: (i) the proposed DP algorithm has a very high time-complexity, therefore it takes time to get the optimal policy for the MU. Therefore, we proposed a low time-complexity heuristic algorithm for the MU. (ii) The heuristic algorithm can compute the policy very fast, and the simulation results have shown that the performance is comparable with our optimal DP algorithm. But we have not theoretically proofed yet that the heuristic algorithm is optimal or near optimal.

7 Conclusion

In this paper, we studied a multi-flow mobile data offloading problem in which a MU has multiple applications that want to download data simultaneously with different deadlines. We formulated the wireless LAN offloading problem as a finite-horizon discrete-time Markov decision process.
A dynamic programming based offloading algorithm was proposed and its time complexity was analyzed. Analysis results showed that the time complexity of the algorithm is rather high. We proposed a low time complexity heuristic offloading algorithm. Extensive simulations have shown that the DP algorithm had the lowest cost, while the heuristic algorithm had comparable performance as that of DP algorithm.
This work assumes that the MNO adopts usage-based pricing, in which the MU paid for the MNO in proportion with data usage. In the future, we will evaluate other usage-based pricing variants like tiered data plan, in which the payment of the MU is a step function of data usage. And we will also use time-dependent pricing (TDP) we proposed in [3][4], without changing the framework and algorithms proposed in this paper. We also assume that the MU can only use one network interface at most, either cellular network or wireless LAN, at each time. In future work, we will relax this assumption to see how the energy consumption and monetary cost will be in this case. Another assumption we have made is that the MU’s mobile probability from one place to another is known. It is reasonable if the MU moves in a certain pattern, for example, people may commute from home to work by the same train at the same time in weekdays. In our future work, we would also like to consider the case wherein the probability of the MU’s movement from one place to another is unknown. The Possible solution is to utilize learning technology to predict the MU’s mobile probability.

Acknowledgements

This work is part of the Grant-in-Aid for Young Scientists (B) research programme with grant number 16K18109, which is financed by the Japan Society for the Promotion of Science (JSPS).

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