2012 IEEE Wireless Communications and Networking Conference: MAC and Cross-Layer Design
AUtility Based Resource Allocation Scheme with Delay Scheduler for LTE Service-Class Support Salman Ali, Muhammad Zeeshan School of Electrical Engineering and Computer Science (SEECS) National University of Sciences and Technology (NUST), Islamabad, Pakistan
, [email protected]
Abstract—LTE standard defines strict requirements for service classes in order to provide end users with exceptional QoS characteristics including fast connectivity and high data rates. However there is no standard scheduling algorithm defined for LTE and the task of protecting end user satisfaction while maintaining service class restrictions is left upon the service provider and currently is an open issue. To address this challenge, in this work we proposed a two-level scheduler with a utility based game theoretic application in the first level that distributes physical resource blocks among classes with different QoS requirements and a delay based air interface scheduling algorithm in the second level that satisfies the strict levels of delay budget requirements defined for LTE classes. A cooperative game is formed between different service class flows by use of a sigmoid utility function that allows for distribution of resources. Lagrangian formulation is used to find the associated Pareto Optimality. The delay based scheduler checks each user’s packet delay in its respective service class and makes scheduling decisions in the downlink direction utilizing current channel conditions. Simulation results carried out with key performance matrices including throughput, packet loss ratio, system delay and fairness index proved the usefulness and efficacy of the proposed approach as compared to existing Proportional Fair, Exponential Rule and M-LWDF algorithms.
different service class in the network  of which some or all may be implemented by service provider. TABLE I.
Guaranteed Bit Rate (GBR)
Packet Error Loss Rate
Conversational video (live streaming)
Real time gaming
Non-conversational video (buffered stream)
The LTE (Long Term Evolution) technology developed by Third Generation Partnership Project (3GPP)  is meant to improve the capability of legacy systems by increasing data rates and extending superior Quality of Service (QoS) support for various multimedia applications. Since the initial release in 2008, a slightly modified version (Release-9) and a complete fourth generation standard named LTE-Advanced (Release10) have been developed. To cater inter-symbol interference and selective fading, LTE uses Orthogonal Frequency Division Multiple Access (OFDMA) in the downlink. Basic LTE network elements consist of a powerful eNodeB (eNB) station and several User Equipments (UEs) in addition to a gateway. The eNB station coordinates with network core via several standard complex protocols. Basic packet scheduling is implemented by the network operator in UE and eNB station for both uplink as well as downlink. However, there are no rigid specifications set by 3GPP for scheduling mechanism leaving the details at the discretion of service provider. Packet Scheduling comes under Radio Resource Management (RRM) and its main functionality is to decide users that would transmit their data on the air interface. The scheduling should integrate fairness in terms of throughput as well as the service policies to which users subscribe . LTE architecture defines a comprehensive table with packet delay budget and packet loss rates for implementing
Video (buffered streaming) TCP-based (e.g., www, e-mail, chat, ftp, p2p sharing, progressive video etc.)
Voice, Video (live streaming, Interactive Gaming)
10-3 300 ms
978-1-4673-0437-5/12/$31.00 ©2012 IEEE
Packet Delay Budget
Keywords - Scheduling, game theory, LTE service class, Quality of Service, delay budget.
LTE SERVICE CLASSES WITH QOS REQUIREMENTS 
Video (buffered streaming), TCP-based (e.g., www, e-mail, chat, ftp, p2p sharing, progressive video, etc.)
To cater different QoS requirements, a number of scheduling algorithms have been defined in literature including the widely adopted M-LWDF, PF, EXP-PF and EXP-RULE schedulers . These schedulers transmit user’s data in a given Transmission Time Interval (TTI) by assigning a calculated priority metric that is specific to the scheduler functionality. However, due to the lack of delay budget and packet loss rate attribute (Table 1), these schedulers are not suited for support of simultaneous Real Time and Non Real Time traffic mix. To prevent bandwidth starvation in terms of Physical Resource Blocks (PRBs) by service classes of low priority, a cooperative game concept has been used in this work. Such a resource starvation phenomenon is inherent to scheduling schemes that do not involve fairness as a function of traffic load in a particular service class. The cooperative game works at a layer before the actual packet scheduling to distribute resources among different classes. This is build upon the concept of “divide and conquer”, where first service classes (inter-class) are sorted to allocate resource blocks and then users in each class (intra-class) are arranged on a delay budget basis for spectrum access. The cooperative game itself refers to an approach where coalitions or group of players are subject to cooperation among themselves. This accounts for a
competition at a coalition level and not at an individual player level. The coalition or group in our case would then correspond to users in a particular service class. The rest of the paper is organized as follows. In section II we discuss the network system model. In section III, related game theory concepts are highlighted. Section IV is committed to discussion of Resource Allocation strategy. In section V we evaluate and compare the performance of our scheduling method with simulation results while in section VI, we conclude the paper with some future directions. II.
Various parameters influence the QoS of LTE service class users in addition to channel conditions, delay requirements and subscription policies. The minimum resource entity that can be allocated to a user is the resource element which when combined together constitutes Physical Resource Block (RB) that stretches across frequency and time domain. In LTE architecture, each RB lasts 0.5ms in time and consists of a grid of 6 or 7 symbols with 12 sub-carriers in frequency domain. The RB spans 180 KHz of bandwidth in length and allocation is done on 1ms basis because of the practical realization of scheduling at every TTI . At each transmission period, UEs inform their instantaneous achievable downlink SNR to eNB station. This value changes as a function of mobility and frequency or time selective fading from multi-path. It is then used to determine the data rate in number of bits for the allocate-able RB. A user ’ achievable data rate for RB at time is calculated as: R, t
where n_bits, n_symbols, n_slots and n_subcarrier are respectively the number-of-bits, number-of-symbols, numberof-slots and number-of-subcarriers. . The effect of path loss and fading are determined for each RB , but remain constant throughout the RB transmission duration. The gain of channel at time t for user i on jth RB as a function of loss is: _
where path_loss and fading are measured in dB scale. Using channel gain, UE determines instantaneous downlink SNR reported to eNB station. The SNR is then calculated as a function of channel gain  using the following formulation: SNR , t
_ N N
Here P is the aggregated power with which eNB station transmits in the downlink side, N is the number of total available RBs, is the neighbouring cell interference and N is a thermal noise measure. III.
UTILITY BASED COOPERATIVE GAME
A cooperative game refers to an approach where coalitions or group of players cooperate among themselves when some action is required to be taken . This refers to a competition between player coalitions that make use of mutual decision making behavior and hence not the decision behavior of individual players. A formally defined cooperative game includes a list of players and some related characteristic functions. If we are given a set of N players, then a coalition is required to shift or transfer benefits among the players. The game is then a set of pairs N, u , where N 1,2, … , n forms
a finite players set and is the characteristic or utility function such that u: 2 . Also n |N| and u 0 0. Coalitions are therefore a subset C N such that N\C is a complement operation for N. When we are given n players, a total of 2 coalitions are feasible. A. Utility function To allow the transfer of benefits, a utility based game approach is adopted in our work. The utility function represents user’s degree of satisfaction  for a particular service class as a function of QoS constraints. Since LTE specifies different characteristics for a large number of different service classes, this complexity of wide service flow characteristics will result in different utility functions for users making the problem and its solution formulation more difficult. So to keep the problem simple, we only consider the network bandwidth dimension which corresponds to the Physical Resource Blocks (PRB) of LTE. The other constraints are dealt with in the scheduling of users. We use a sigmoid utility function  to reflect different service class user’s resource requirements. The sigmoid utility function is formulated as 1
1 1 1 1
where is the sigmoid utility as a function of players data rate, and reflect the priority type and intrinsic resource requirement of the service class (see Table 1, priority and example services column) user and , are constants used to normalize utlity function. For a real time connection like VoIP or streaming video with fixed QoS constraints, will decide the parameter and 0 . The parameter is decided by the combination of and ( corresponds to Guaranteed Bit Rate GBR and for Maximum Bit Rate MBR for LTE network). For best effort traffic (like web browsing or FTP) which corresponds to NGBR class of LTE, the parameter is set to 0. Only the parameter is used to determine the user’s service elasticity and priority type. The utility function thus has in itself the ability to depict user’s service features like resource requirements, adaptability and elastic properties. B. Game Formulation Since the resources have to be shared between LTE service classes, the limited resource pool always falls short of the requirements. So to avoid a situation in which a high service class completely starves a low service class, a cooperative game can be formed and implemented at the eNB station that maximizes the utility function while allocating exactly divisible PRBs for downlink traffic. Let the number of classes be . The PRBs are distributed among classes with N 1,2, … , n forming a represents finite players set. For each class 1,2, … , the data rate in terms of resources that are assigned to class users. Based on this, the strategic game form is defined as:
• • •
Players: The service class users N 1,2, … , n Strategies: The resource assignment vector for users 1,2, … , Payoffs: The sum of users utility function
The payoff revenue for a player , is computed from the sum of utility function for that class and is given as R d
f .U t ,r ,d
where is the total number of flows or connections in the class that belongs to. is the utility function defined in equation (4) and , parameters classify the users service priority. The total network profit is defined as a function of the payoffs for all users in all classes. F
f .U t ,r ,d
C. Network Profit Optimization We defined an optimization formulation from the payoffs and total network profit. The purpose of this is to maximize the total payoff profit of the system which in turn maximizes the system throughput. The maximizing framework is defined as: F
R d ∑F f
f .U t ,r ,d
Here Cp denotes the networks total available system capacity. The optimal solution of a cooperative game is the Pareto optimality which we define as follows: P d d , d , … . dF
P d d , d , … , dF
Since we use a delay scheduler and Utility value function, we call our proposed methodology as U-DELAY. The allocation or resource distribution is done by splitting the complexity in two steps for each transmission interval. At first step, resource distribution is done among classes using Sigmoid Utility function approach and then at the second step a delay budget based scheduler is used to select users for transmission. This minimizes the complexity of allocation by following a divide-and-conquer policy where at first step an inter-class resource distribution is accomplished and at the second step an intra-class user selection is targeted.
f .U d
where 0 is the Lagrange multiplier that represents the network resource prices and is associated with a linear constraint of capacity. Decomposing further F
f U d
L d, λ
The function , now only depends upon the user of a specific class’s bandwidth or network resource allocation and the network resource price . Lagrangian dual function for the problem is defined as the maximization of , over for a given value of . For all valid , each service class maximizes . over . Since the utility function itself is a sigmoid and not a concave function, the maximum and minimum resource allocation constraints and can be obtained through utility functions parameter and . Under (d , d ) we modify (10) as F
f U d
L d, λ
L d, λ
where d d , d , … . dF is the Pareto optimality and the solution for (8) if all d d , d , … , dF satisfy F d T Cp. Hence the cooperative game is equal to an optimization problem to be solved at the eNB station for resource distribution in the downlink. IV.
A. First Step In the first step to divide resources among service class users, Lagrangian optimization approach  is used to reduce the complexity in finding the Pareto optimal solution and to make the problem a convex optimization. From equation (7), the Lagrangian is defined as
arg max U d
d, λ d
A sub-gradient is used to update the dual variable resolve the Lagrangian
d λ m
In equation (13) represents the iteration number while ∆ is the step size. Equations (12) and (13) can be used to solve network profit optimization problem globally and get optimal resource allocation vector that is Pareto optimal for the game with the corresponding network optimal resource price . B. Second Step After the inter-class resource distribution is done, the next step is to choose users in a specific class for scheduling on air interface. The intra class user assortment is done on delay measurements as a function of the budget described in the LTE class table (Table 1). For this purpose, a Head of Line (HoL) packet delay is measured which is defined as the difference in time measures between the current packet serving time and the time stamp it first arrived at the MAC buffer queue. This time is then compared with the delay budget measures of the specific class the user belongs to. The packet whose delay difference of HoL delay and class budget is the lowest is scheduled first. If the difference goes below zero or is a negative value, this means that the threshold is exceeded and packet is dropped. In addition, LTE standard mandates the use of Channel Quality Index (CQI) for efficiency which we incorporate as SNR values in the scheduling.
Figure 1. Steps in Utility Based Game Theoretic Resource Allocation Method
A. Performance Measures We use throughput, fairness index, system delay and packet loss ratio for performance analysis. These are defined and explained below: The throughput of the system is defined as the summation of the packets that are transmitted in a time interval from all the UE to eNB station or from eNB to all UEs. Since we cater for downlink only, therefore the latter case is measured only. A certain portion of the total packets accounts for overhead, thereby reducing the good-put, but we consider here the collective throughput. In mathematical terms, the aggregate system throughput  is defined as system throughput
where T is the total time utilized in simulation and p represents the size of the packet in bits transmitted from eNB station to a particular user i summed over a time interval. K corresponds to total users of a service class that receive packets from eNB. Since we are using the scheduler based on a delay metric, it is essential to analyze the overall delay experienced by the system as compared to other methods. The system delay is calculated as an average of the combined time delay difference between the packet arrival in queue and the time it is transmitted. This value adds up to the HoL packet delay and is then averaged over all packets. Mathematically, system delay  is measured as Figure 2. Flow Chart highlighting Second Step of Delay Based Scheduling
Let the delay-budget of packet for a service class i be represented by σ where i F. Then for any use j in i F, the HoL time delay t is represented as: HoL t
where T represents the time of the packet since it arrived at the scheduling queue and T is the current packet processing time. The remaining time for scheduling or the delay metric is then the function of HoL: delay t
The difference σ HoL t is only feasible for positive values, i.e. σ HoL t 0. This means that any packet that crosses the budget is dropped. For final RB allocation, the user with the lowest delay t metric is chosen. u
arg min delay t
Once the user u is selected for RB allocation, the SNR values received by that user are utilized and the highest of these is used to decide the actual RB on which the the user should transmit. Various stages in step 2 of intra user selection are shown in Fig 2A as a flow chart. V.
We use a discrete time event simulator developed in C++ with LTE specifications and attributes for analysis . The parameters for LTE system including data traffic and other performance measure metrics are described below:
Here HoL is the same as described earlier, and K is the total number of users with service flows while T being the total simulation time. Fairness is an essential metric for scheduling performance analysis because the resource allocation done at the first level adopt utility value method that may alter fairness. Fairness can’t be measured directly since at a lower level the scheduler enforces an intra user selection method on delay basis for RB allocation. Therefore to estimate the effects of first level utility function, a system level fairness metric is used. We define it mathematically as p_sizemax p_sizemin fairness 1 19 ∑K ∑T p_sizei where p_size p_size is the difference in total packet sizes of the most and least served user service flows over some time period T . ∑K ∑T p_size amounts to the total accumulated packet size of the flows that arrived at eNB scheduler over time T. Finally the packet loss ratio is defined as the ratio of total packets dropped as a result of exceeding time delay to the aggregated packet size of all the packets reaching eNB MAC buffer queue over some simulation time T 
∑K ∑T p_discardi t ∑K ∑T p_sizei t
400000 350000 U-Delay PF M-LWDF EXP-RULE
300000 250000 200000
40 50 Users
Figure 3. Average Throughput for Video 350000
0.6 Packet Loss Ratio
300000 250000 U-DELAY
System Delay (ms)
Figure 10. Average System Delay
B. Simulation Environment For simulation, we use LTE-Sim , a discrete time event simulator build in C++. The network setup consists of a single cell network with some interference noise. There are four service flow types in the network with basic requirements of 440kbps for trace based video data, 300kbs for interactive gaming data, 8 kbps for VoIP service and CBR traffic at 3kbps. The users are taken in a mixed proportion with 30% for Interactive Gaming, 30% for Video, 25% for VoIP and 15% constituting CBR traffic. VoIP class is taken as GBR while the other classes are specified as Non-GBR type. User’s mobility is defined by random directions averaging at a speed of 3km/hr. Transmission time interval occurs after 1 ms time interval. The LTE frame is formed by 5 such consecutive TTIs and within each 1ms time slot, 14 OFDM symbols can be used. The System Bandwidth for simulation is 15MHz which includes 75 discrete Physical Resource Blocks in the downlink. The propagation loss model includes shadowing (with 0dB mean and 8dB standard deviation for log normal distribution), multipath (Jakes model), penetration loss (12dB) and simple path loss (measured as a function of distance form eNB terminal). C. Simulation Results
Figure 8. Average Packet Loss Ratio
40 50 Users
Figure 6. Average Throughput for VoIP
40 50 Users
U-Delay PF M-LWDF EXP-RULE
U-Delay PF M-LWDF EXP-RULE
Figure 7. Average Throughput for Gaming
40 50 Users
Figure 4. Average Throughput for CBR
9100 Throughput (bps)
3200 Throughput (bps)
M-LWDF EXP-RULE 10
Figure 9. Average Fairness Index
Game Theory with sigmoid utility value characteristic function and a delay based scheduler at the MAC layer is used in this work to support LTE service class scheduling. Algorithms namely M-LWDF, PF and EXP-RULE have been compared with to score our scheduling scheme. The PF scheduler allocates resources to users on the basis of channel quality measures of user and the past running throughput the user maintained. The general goal in PF is to maximize aggregated throughput of the system. The M-LWDF scheduler can serve users with varying QoS requirements. Best channel conditions and the highest Head of Line packet delay of users is used to achieve prioritization of service class. The EXPRULE uses a metric measure that increases priority of real time flows as compared to non-real time flows while the delay threshold approaches. Results for average throughput of service flows of Video, Gaming, VoIP and CBR against the number of users are analyzed. In CBR traffic comparison, for an average 30 users the throughput of the four schemes remains almost consistent with each other but after that EXP-RULE deviates most while the other three algorithms show better performance with UDELAY performing superior to all (Fig 4). The average throughput for VoIP flows shows some variations for the four schemes (Fig 5). Here EXP-RULE performs fairly similar to U-DELAY scheme. For an average initial 40 users, PF and MLWDF perform comparatively low but after that the performance is closer to U-Delay. For Video and Gaming requirements the throughput of the four schemes do not diverge much for an estimated 20 to 30 users, but when more users enter the network, the performance of U-DELAY outweighs the other three schemes with PF showing worst performance (Fig 3 and 7). For Packet Loss Ratio case (Fig 8), the PF scheme performs poor when more than 20 users on average enter the system while U-DELAY maintains a significant space and introduces only around 24% loss percentage for more than 80 users making the performance
much visible. For system delay measures (Fig 10), U-DELAY performs much better than other schemes for average 60 users but after that the delay of the system cannot be maintained while EXP-RULE and M-LWDF perform better at this stage. The rationale for such behavior is the fact that when network load increase, delay requirements become much tighter to be met and more packet are lost when delay thresholds reach early. To counter it, admission controller can be modified to limit the users according to available system capacity. In Fairness Index comparison (Fig 9), the use of QoS constraint based Sigmoid Utility function shows proficient results depicting scores as high as 0.88 at 80 system users for UDELAY while PF scheme score drops to a considerable 0.47 margin. VI.
The LTE standard defines classes with strict requirements in order to provide QoS with fast connectivity and high data rates. In this work, we proposed a two-level scheduler with game theoretic approach that distributes physical resources among classes with a sigmoid utility function at first level and then an implementation of a delay based scheduler at the MAC layer to satisfy diverse levels of delay budget requirements of LTE classes at the second level of proposed architecture. Cooperative Game is formed between service class flows of users by use of bargaining that allows for distribution or allocation of physical Resource Blocks in a QoS restricted manner. The delay based scheduler checks each user’s packet delay budget in relation to the LTE service class and makes scheduling decisions in the downlink utilizing current channel conditions experienced by user. Simulation results carried out with key performance matrices including throughput, packet loss ratio, and system delay and fairness index showed that the proposed two-level resource allocation scheme performs better than existing simple Proportional Fair, Exponential Rule and M-LWDF algorithms. Proposed scheduler out performs all existing techniques in throughput performance specifically when the number of users in the system exceed on average of 30 mixed service users. Among all the schemes, PF performs with the lowest rank while EXPRULE performs next to our approach. However, EXP-RULE does not perform well for GBR based Constant Bit Rate (CBR) traffic when the number of users is high, while the UDELAY performs the best. The fairness results show that our proposed U-DELAY scheme gives a score of 0.88 even when the system users are as high as 80, while other approaches drop down to around 0.84 or less. The system delay analysis depicts satisfactory performance of proposed U-DELAY for around 70 users in the system. As a final comment, the scheme can be used for supporting both real time and non-real time traffic with promising results for QoS and user satisfaction. In future, we intend to investigate interference issues in resource allocation and scheduling for LTE.
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