Opportunistic Scheduling: an Illustration of Cross-Layer Design
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Opportunistic Scheduling: An Illustration of Cross-layer Design Xin Liu Ness B. Shroff Edwin K. P. Chong Computer Science Dept. Dept. of Electrical & Computer Engineering Dept. of Electrical & Computer Engineering Univ. of California, Davis Purdue University Colorado State University
Abstract TCP modifications for energy efficiency. 3) Network layer and data link layer. For instance, link reliability The unique characteristics of wireless information can facilitate routing decisions. 4) MAC communication systems - namely, timing-varying and physical layer, which is the focus of this paper. channel conditions and multiuser diversity - call for The basic idea of “opportunistic scheduling” that will specifically tailored system designs. In this paper, we be overviewed in this paper is allocating resources to overview a cross-layer design method, named links when they experience good channel conditions opportunistic scheduling, for exploiting the time- while avoiding allocating resources to links when varying nature of the radio environment to increase they experience poor channel conditions, thus the overall performance of the system under certain efficiently utilizing radio resources. This is also QoS/fairness requirements of users. We first discuss referred as channel-aware scheduling or exploiting a general system model, and the fairness and QoS multi-user diversity. We use the term opportunistic constraints being considered. Then, we present to denote the ability to schedule users based on various optimal index policies and discuss their favorable channel conditions. On the other hand, the properties. We also outline a methodology to potential to transmit at higher data rates implement these opportunistic scheduling solutions opportunistically (i.e., when channel conditions in practice. Lastly, we discuss the advantages and permit) also introduces an important tradeoff between costs associated with opportunistic scheduling, and wireless resource efficiency and the level of identify possible future research directions. satisfaction among different users. For example, allowing only users close to the base station to 1. Introduction and Literature Review transmit at high transmission power may result in very high throughput, but sacrifice the transmissions Built upon the success of second generation cellular of other users. Such a scheme cannot satisfy the services, tremendous amounts of resources have increasing demand for quality of service (QoS) been invested into 3G systems, especially in Asia, by provisioning in the emerging high-rate data wireless companies such as SK Telcom and NTT DoCoMo. networks. To address this problem, we present here a Further, other wireless systems, including WLAN, framework for scheduling users in an opportunistic ad-hoc networks, and wireless sensor networks, are way. The objective is to improve wireless resource rapidly proliferating. In summary, the demand for efficiency by exploiting time-varying channel wireless data services is skyrocketing and there is a conditions while at the same time controlling the real need to optimally design and engineer wireless level of fairness and QoS among users. systems.A major challenge is that wireless com- munication requires sharing a limited natural resource: the radio frequency spectrum. The data-rate 1.1 Literature Review capacity that a radio frequency channel can support is limited by Shannon’s capacity laws. Hence, in the Wireless scheduling schemes have attracted a lot of wireless environment, one has to engineer the recent attention. First, the scheduling policies of network very carefully so that little, if any, wireless wireline networks are extended wireless networks. spectrum is wasted. The proposed wireless scheduling schemes provide various degrees of performance guarantees, including Compared with the wired counterpart, wireless short-term and long-term fairness, as well as short- systems have some unique characteristics, namely term and long-term throughput bounds. A survey of scare resource, time-varying and location dependent these algorithms can be found in [1]. However, these channel conditions. The nature of the wireless efforts model a channel as being either “good” or medium makes it particularly attractive for cross- “bad,” which may be too simple to effectively layer design. Different layers have been considered, characterize realistic wireless channels, especially for as illustrated by the following examples. 1) data services. Application layer and network layer. For instance, a multimedia server can adjust the coding scheme In [2, 3], the authors present a scheduling scheme for based on available bandwidth by tracking packet the Qualcomm/HDR system. Their scheduling losses. 2) Transport layer and network layer, e.g., scheme exploits time-varying channel conditions while maintaining “proportional fairness,” as defined as well as some precautionary notes and possible in [3, 4]. future research directions. This is followed by a conclusion in Section 5. All the results are presented In [5, 6, 7, 8], the authors study scheduling without proofs. We refer readers to the corresponding algorithms for the transmission of data to multiple papers for reference. users. Both delay and channel conditions are taken into account. Throughput optimality is defined in [6] 2. System Model and Constraints as follows: a scheduling algorithm is throughput 2.1 System Model optimal if it is able to keep all queues stable if this is at all feasible to do with any scheduling algorithm. We consider a time-slotted system where time is the Furthermore, the authors of [9] investigate a resource to be shared among all users. The system scheduling algorithm to maximize the minimum can have more than one channel (frequency band), weighted throughput of users. We discuss these but at any given time, only one user can occupy a schemes in more detail later. given channel within a cell. Here, we focus on the scheduling problem for a single given channel. Such In [10, 11], we present a framework for opportunistic a system model includes TDMA systems as well as scheduling. In particular, the overall performance of time-slotted CDMA systems (an example of the latter the system is maximized under certain QoS/fairness is the IS-856 system, also known as HDR). requirements of users. Channel conditions in wireless networks are time- Opportunistic scheduling exploits the channel varying, and thus users experience time-varying fluctuations of users. Thus a natural question to ask is performance. We use a stochastic model to capture what we should do in environments with little the time-varying and channel-condition-dependent scattering and/or slow fading. In [12], the authors performance of each user. Specifically, following the present a scheme that uses multiple transmission k antennas to “induce” channel fluctuations, and thus approach of [12], let {Ui } be a stochastic process exploit multi-user diversity. Further, such a scheme k associated with user i , where U is the level of can also be used opportunistically to null inter-cell i interference. performance that would be experienced by user i if k In [13], scheduling problems for real-time traffic are it is scheduled to transmit at time k. The value of Ui studied. The authors show that the greedy algorithm measures the “worth” or “utility” of time-slot k to the is 1/2 competitive against the offline optimal user i, and is in general a function of its channel algorithm. Further, they show that no deterministic condition. The better the channel condition of user i, online algorithm can achieve a competitive ratio the larger the value of U k . Examples of the value of higher than 1/2. i U k are throughput, the value of throughput minus Opportunistic scheduling has also been studied under i various scenarios, including distributed systems, the cost of power consumption, etc. We assume that (e.g., [14, 15, 16],) systems with multiple input and k Ui is nonnegative and bounded. For simplicity, we multiple output (MIMO) antenna arrays, (e.g., [17, k 18, 12],) multi-carrier systems, (e.g., [19],) sensor assume that {Ui } is stationary and ergodic (this networks, (e.g., [20],) multi-hop wireless systems, assumption can be removed in some case, e.g., see (e.g., [21, 22],) and with power and rate control, (e.g., [11]). For convenience, we use the notation [23, 24, 25]). A cautionary note on cross-layer design U {U ,,U }, where U is a random is presented in [26]. A thorough analysis on user – 1 N i level performance is given in [27]. variable representing the performance value of user i at a generic time-slot. Note that the stationary 1.2 Organization assumption does not preclude correlations across This paper overviews the concept of opportunistic users or across time and moreover this assumption scheduling and how it can be used to improve system can be relaxed, as in [11]. efficiency as well as provide adequate QoS. In Wireless spectrum is a scarce resource, hence Section 2, we provide a general system model, and improving the efficiency of spectrum utilization is the fairness and QoS constraints being considered. important, especially to provide affordable high-rate- Then, in Section 3, we present various optimal index data service. However, a scheme designed only to policies and discuss their properties. In Section 3, we maximize the overall throughput could be unfairly also outline a methodology of how to implement biased, especially when there are users with widely these opportunistic scheduling solutions in practice. disparate distances from the base station. To address In Section 4 we provide a discussion of various issues this problem, we introduce QoS/fairness requirements into the framework of opportunistic Throughput maximization In this case, the only scheduling— our goal is to maximize the system objective is to maximize the overall system performance (defined later) by exploiting time- throughput regardless the performance of each varying channel conditions while maintaining certain individual user. In other words, each user is user-oriented constraints. Examples of such guaranteed zero percent of the system throughput. In constraints include long-term and/or short-term this case, a small number of users with very good fairness constraints or (direct) performance channel conditions may consume all the resource and constraints. starve other users. A scheduling policy is a rule that specifies which user Max-min fairness The objective of the throughput is scheduled at each time-slot. For simplicity of max-min fairness is to maximize the minimum notation, let Q(U) be the decision of a stationary throughput of all users. Let N be the number of users in the system. Each user is guaranteed 1/N portion of policy Q at a general time-slot where U is the the system throughput. This objective is “absolutely” fair. However, when there are users with very poor performance value of users. At a generic time-slot, if a policy Q schedules user i Q(U) {1,..., N} channel conditions, to achieve max-min throughput fairness will cause significant system performance to transmit, then the system receives a “reward” of penalty. E(U ) U i . Note that Q(U ) is the average system Proportional fairness: Proportional fairness (PF) performance value associated with policy Q, and it is scheduler maximizes the product of the throughput the sum of all users’ average performance values delivered to all the users. In other words, the set of throughput achieved by different users is (where we reap a reward of Ui only if user i is proportionally fair if increasing the throughput of one scheduled). The objective is to find a policy Q that user from the current level by x% requires a maximizes the average system performance value cumulative percentage decrease in all the users of E(UQ(U ) ) under the constraints. In this paper, we more than x%. Proportional fairness presents a focus on stationary policies. Extensions on more tradeoff between the overall throughput and each general policies, including non-stationary and non- user’s throughput. causal policies, can be found in [11]. Temporal resource-sharing fairness: In this case, We are interested only in policies that satisfy specific each user is guaranteed a certain portion of the QoS/fairness requirements. We say that a policy Q is resource, i.e., time-slots. Note that temporal resource- feasible if it satisfies the constraints for all users. Our sharing fairness is different from the utilitarian goal is to find a feasible policy Q that maximizes the fairness. In wireline networks, when a certain amount system performance, which may be defined of resource is assigned to a user, it is equivalent to differently under different assumptions. granting the user a certain amount of throughput/performance value. However, the We focus on the downlink of a wireless network. The situation is different in wireless networks, where the base station serves as the scheduling agent. The amount of resource and the performance value are scheduling scheme does the following: at the not directly related (though closely correlated). By beginning of a time-slot, the scheduler (i.e., the base limiting the resource of each individual user, a user is station) decides which user should be assigned the guaranteed a certain throughput (based on its channel time-slot based on the performance values of the conditions). Resource consumed by a user can be users at that time-slot. If a user is assigned a time- directly connected with the price the user should pay. slot, then the base station will transmit to the user in Premium users will obtain better services in a that time-slot. In general, downlink transmission is stochastic sense. more important for data traffic because of the highly asymmetric nature of the data service. Minimum data-rate constraints: In this case, each user is guaranteed a minimum data-rate. This type of 2.2 Fairness and QoS Constraints QoS constraint is desirable for users, but difficult for We first summarize the fairness and QoS constraints the system where feasibility is a major concern. discussed in the paper. 3. Optimal Scheduling Policies Utilitarian fairness: In this case, each user is A common objective of opportunistic scheduling is to guaranteed a certain portion of the total system maximize the system performance given the throughput. Two extreme cases of utilitarian fairness fairness/QoS constraints. To maximize the system is the max-min throughput fairness and system performance is formally presented as throughput maximization. max E(U ) . fairness constraint, and the greater the opportunity to Q Q(U ) improve the system performance. * Let Ti (Q) E(Ui 1{Q(U ) i}) be the throughput An optimal policy Q is defined as follows: of user i under policy Q where 1{.} is the indicator * * , function. We have Q (U) arg maxi (ui Ui )
N * T (Q) T (Q) E(U ). where the ui s are real parameters satisfying i1 i Q(U ) * Of course, the values of T (Q) depends on the a) mini (ui ) 0 ; i distribution of , which is ignored in the notation * U b) for all i, P{Q (U ) i} ri . for simplicity. In this section, we summarize some c) for all i, if * then * =0. results in opportunistic scheduling. It is interesting P{Q (U ) i} ri ui that optimal policies turn out to be simple, easily Let us explain the heuristics of the policy Q* , which implementable index policies under various fairness and QoS constraints. is helpful to understand the intuition of opportunistic scheduling. For a proof of the optimality of * , we 3.1. Temporal Fairness Q refer readers to [11]. We can think of the parameter Because time is the resource shared among users, a * natural fairness criterion is to give each user at least a ui above as an “offset” used to satisfy the fairness certain share of the entire resource, i.e., time. Let r requirement. To elaborate, consider the case where i we want to maximize the overall performance denote the minimum time-fraction that should be without any QoS requirements. It is straightforward N to show that we should always choose the “best” user assigned to user i, where ri 0 , ri 1, and i1 (i.e., the user with the maximum performance value) N is the number of users in the cell. Here, we assume to transmit. In other words, Q* (U ) arg max U . that the r s are predetermined and serve as pre- i i i However, such a scheme may be unfair to certain specified fairness constraints. The value of ri users. Hence, to satisfy the fairness requirement, the dictates the minimum fraction of time that a user scheduling policy schedules the “relatively-best” user should transmit on the channel, which is typically to transmit. User i is “relatively-best” if determined by the user's class, the price the user is * * * ui Ui u j U j for all j. If ui >0, then user i willing to pay for the wireless service, or the user's is an “unfortunate” user, i.e., the channel condition it current channel conditions. The scheduling experiences is relatively poor. Hence, it has to take algorithm then decides which time-slot should be * assigned to which user, given the minimum time- advantage of some other users (e.g., users with u j fraction requirement. Our goal is to develop a =0) to satisfy its fairness requirement. Thus, to scheduling policy Q that exploits the time-varying maximize the overall system performance, we can channel conditions to maximize the total expected only give the “unfortunate” users the amount of system performance while satisfying the resource- resource equivalent to their minimum requirements. sharing constraint. The problem can be stated * Last, when P{Q (U ) i} ri for user i, the user formally as follows: gets more than its minimum requirement---this user * maxQ E(U Q(U ) ) cannot take advantage of other users, i.e., ui =0. In summary, condition (a) above on u* is for subject to P{Q(U ) i} r , i 1,2,...N i i normalization and condition (b) is the feasibility In words, the problem is to find an optimal policy requirement. Condition (c) is important to the among all policies such that the total system optimality of Q* . Its heuristic interpretation is that a throughput is maximized where each user’s resource- good user that gets more than its minimum sharing requirement is satisfied. Note that requirement cannot take advantage of other users. N : r 1 is a tuning parameter such that the This condition can also be explained in terms of i1 i complementary slackness: if the constraint is not smaller the value of , the less restrictive the active (i.e., the average performance of user i is greater than its minimum requirement), then the corresponding u* (which can be interpreted as a The authors of [9] consider a special case of the i above opportunistic scheduling problem. Lagrange multiplier) is zero. Specifically, they consider maximizing the minimum weighted performance of users. This is a special case Property: If the performance values U s, i of the utilitarian fairness problem defined in this i 1,2,...N, are independent, then section. T {Q} P{Q(U ) i}U rU , i 1,2,...N. This problem setting requires fairness in terms of i i i i performance values, which, to some extent, parallels This property makes a strong statement about the the concept of weighted fair queueing used in individual performance of each user. If users’ wireline networks. The difference is that the overall performance values are independent, the average capacity here is not fixed; it depends on channel performance of every user in our opportunistic conditions, the values of ai , and the scheduling scheduling scheme will be at least that of any non- policy. opportunistic scheduling scheme. In this sense, the * opportunistic scheduling policy does not sacrifice any The parameter vi can be considered a “scaling” used user’s performance to improve the overall system to satisfy the utilitarian fairness constraint. The performance. Of course, different users may optimal scheduling policy always chooses the experience different amounts of improvement. This relatively-best user to transmit. In this case, a user is property can also be explored to provide direct relatively-best if performance guarantees to users with simple resource allocation schemes. * * (b v j )U j arg maxi (b vi )Ui . * The values of the ui s are determined by the * As before, if vi >0, then the user is an “unfortunate” distribution of U and the values of the ri . In user, and its average performance value equals the practice, the distribution of U is unknown, and minimum requirement. * Utilitarian scheduling schemes have certain notable hence we need to estimate the parameter ui . features. First, the utilitarian fairness constraint Similarly, in the opportunistic scheduling schemes controls the maximum discrepancy of performance discussed in other sections, there are also parameters values among users. Second, the constraint given that need to be estimated. Estimations of the ensures that a user is given at least a certain share of parameters are discussed in Section 3.5. the total performance, and is hence more suitable in 3.2. Utilitarian Fairness some situations than the temporal fairness constraint. However, there is also a significant disadvantage of a The problem formulation of the utilitarian fairness is utilitarian scheduling scheme: a user experiencing presented as poor channel conditions could have a detrimental max T (Q) impact on the overall system performance because a Q substantial portion of the total time-slots may have to be allocated to this user in order to meet its fairness subject to T (Q) a T (Q), i 1,2,...N , i i requirement. To alleviate this potential problem, one N can devise an adaptive threshold strategy [11]. where a 0, and a 1. i i1 i 3.3 Minimum-performance Guarantee An optimal policy is defined as follows: Thus far, we have discussed two optimal scheduling * * schemes that provide users with different fairness Q (U) arg maxi (b vi )Ui guarantees. From a user’s viewpoint, a more direct QoS is defined in terms of minimum-performance N where b 1 a v* , and the v* s are real guarantees. To elaborate, the objective is to i1 i i i maximize the average system performance subject to parameters satisfying meeting each user's minimum-performance * requirement, formulated as: a) mini (vi ) 0 ; * * b) for all i, Ti (Q ) aiT(Q ); maxQ T (Q) * * * c) for all i, if Ti (Q ) aiT (Q ); then vi =0. subject to Ti (Q) Ci , i 1,2,...N where C is the minimum-throughput requirement of * * i Q (U ) argmaxi i Ui user i. Consideration of this problem raises two questions: (i) Is the requirements feasible, i.e., does is optimal for many types of scheduling problems. For example, the optimal utilitarian policy defined there exist a policy such that Ti (Q) Ci , for all i? earlier is in this form. If * 1 for all i , then the (ii) If it is feasible, which policy maximizes the i overall performance under the given QoS policy maximizes the total system throughput. On the * * requirement? other hand, if i 1/Ti (Q ) for all i , then the Compared to fairness requirements, the formulation policy is proportional fair [2]. here offers users a more “direct” service guarantee. In [5,6], the authors study scheduling algorithms For example, if the performance measure is defined where both delay and channel conditions are taken as the data-rate, then each user is guaranteed a into account. Roughly speaking, the algorithm is: minimum data-rate, which may be more important to a user than knowing that a minimum amount of Q* (U) arg max *U W , resource will be assigned to it. While appealing to i i i i users, providing minimum-performance guarantees where W is the head-of-the-line packet delay for can be quite difficult in practice because of the i * feasibility issue---can the system satisfy the queue i, and i is some constant. The policy is performance requirements for all users? (Note that throughput optimal. feasibility is not a concern in the fairness-based constraints.) More discussion on feasibility can be We have presented a framework for opportunistic found in [11]. There are, however, some natural scheduling and studied different scheduling settings where feasibility is not a problem. For problems. These scheduling problems share a example, the requirements can be set as the average common goal: to improve the spectrum efficiency data rates in a non-opportunistic round-robin while maintaining certain levels of QoS for each user scheduling scheme. Then, it is guaranteed to be using opportunistic scheduling algorithms. The feasible for opportunistic scheduling policies. solutions to these scheduling problems turn out to be index policies---all the schemes choose the An optimal policy is defined as follows: “relatively-best” user to transmit. Although Q* (U ) arg max *U “relatively-best” has a different meaning for each i i i scheduling policy, the basic idea is to use an offset or a scaling to satisfy the QoS requirements for users. In where * s are real parameters satisfying i general, the larger the number of users sharing the * same channel, or the larger the variance of U , the a) mini (i ) 1; * larger the “opportunistic” scheduling gain compared b) for all i, Ti (Q ) Ci ; with non-opportunistic scheduling policies. c) for all i, if T (Q* ) C , then * =0. Furthermore, the more restrictive the QoS constraint, i i i the less the flexibility for opportunistic scheduling The parameter * “scales” the performance values decisions, and the lower the system performance i gain. of users, and the scheduling policy schedules the relatively-best user, where a user is relatively-best if 3.5 Implementation * * jU j arg maxi i Ui . If the scaling factor for a Figure 1 shows a block diagram of a practical user is larger than 1, then the user is an “unfortunate” scheduling procedure that incorporates on-line user, and it is granted only an average performance parameters estimation. In our scheduling policy, the value that equals its minimum-performance base station needs to obtain information of each requirement. The opportunistic scheduling policy user’s performance value at a given time slot to make always provides “no-worse” performance values for the scheduling decision. At a time slot, a user could each user relative to that of the non-opportunistic measure the received signal power level (from the scheduling policy, assuming that the signaling cost is user’s base station) and the interference power level. negligible. Thus, the opportunistic scheduling policy Based on the estimated SINR, the user can then dominates non-opportunistic policies. obtain its performance value. The information is sent back to the base station, which can be accomplished 3.4 Index Policies in several ways. For example, each user could It turns out that a scheduling policy of the form of maintain a small signaling channel with the base station. Alternatively, the required information could be piggybacked over the user’s acknowledgment k k k ei gi fi (u ) packets. Then the base station makes the scheduling decision based on the scheduling policy and transmits k k k k (ui min j u j )(1{Q (U ) i} P{Q (U ) i}) to the selected user. Last, parameters used in the scheduling policy are updated, which is discussed which is an unbiased estimate. Hence, we can use a next. stochastic approximation algorithm of the form
k 1 k k k ui ui gi , where, e.g., k =1/k.
k k When ui min j u j , we also need to ensure that Figure 1. Block diagram of the scheduling policy k k P{Q (U) i} ri . If P{Q (U) i} ri , then with on-line parameter estimation. u k is an infeasible parameter vector, which causes some fairness constraint to be violated. To ensure The opportunistic scheduling policies described in that u k converges to u* , we should project u k previous sections all involve some parameters that onto the feasible set of u s. However, because we do need to be estimated online. Such parameters are determined by the values of the QoS requirements not have knowledge of the distribution of U , it is and the distribution of the utility values. In practice, very difficult to find the exact projection. Hence, we such a distribution is a priori unknown, and hence we use the following intuitive algorithm as a projection. need to estimate the parameters. In this section, we k use the temporal fairness scheduling scheme as an It is easy to see that P{Q (U) i} is an increasing example to describe briefly how to estimate these k k k function of u . Hence, if ui min j u j , and parameters efficiently via stochastic approximation i techniques. Similar estimations can be applied for k P{Q (U) i} ri , then we increase the value of other scheduling policies. uk to increase the value of P{Q k (U ) i}, as a Recall that the parameters are chosen to satisfy the i projection to the feasible set. Although we do not following requirement: for all i, if * know the value of P{Q k (U ) i}, we can estimate P{Q(U ) i} ri then ui =0. Hence, we can write k f (u) 0 it by a moving average. Let pi be the estimate of as a root of the equation , where the ith component is given by k k P{Q (U) i}. We update pi in each time-slot f (u) (u min u )(P{Q(U ) i} r ) , as follows: i i j j i k k 1 k where i=1,2,…N. Next, we use a stochastic pi (1 w) pi w1{Q (U ) i}, approximation algorithm to generate a sequence of where w is a constant, indicating how fast pk tracks iterates u1 , u 2 , u 3 , … that represent estimates of i k k k * k k k u min u , u . Each u defines a policy Q given by P{Q (U) i}. If pi ri , and i j j k k k Q (U) arg max (U u ) . To construct the then we increase the value of ui by a small constant. i i i stochastic approximation algorithm, we need an By doing this, we push u k towards the feasible set of estimate of f (u k ) . Although we cannot obtain u s. Simulations indicate that this approach works well. f (u k ) directly, we have a noisy observation of its components: k k k k 4. Discussion gi (ui min j u j )(1{Q (U) i} ri ) , Different schemes may be suitable for different where i=1,2,…N. The observation error in this case is scenarios. For example, if the service provider wants to build a simple wireless network with pricing, the temporal fairness scheduling scheme is a reasonable choice. The temporal fairness scheduling scheme is simple and flexible without feasibility concerns. The of channels. In general, the greater the fluctuation of amount of resource consumed by a user determines channel conditions, the larger the number of users, the minimum performance the user gets (with the better the performance gain. technical assumptions). The resource consumed by a Another concern in opportunistic scheduling is the user can be connected directly with the price the user time scale of fluctuation. The fluctuation of channels should pay. On the other hand, the minimum- should be slow enough for users to estimate and performance guarantee scheme provides users a exploit it. On the other hand, the fluctuation should direct performance assurance, but involves the be fast enough, so that users won’t experience additional complication of feasibility. If the service extreme long delays. Though many data users are provider wants to build a network that provides data- delay-tolerant, extreme delays may cause upper- rate guarantees, then this scheme is an appropriate layer problems such as TCP timeout. choice. However, in practice, the feasibility issue may be difficult to handle, especially in a wireless There is a tradeoff between scheduling gain and setting, and providing service performance short-term performance. In general, the stronger the guarantees is challenging in both wireless and time-correlation of channel conditions (i.e., the wireline networks. slower the channel fluctuation), the worse the short- term performance, and the greater the improvement It should be noted that the framework for in the short-term performance, the less the scheduling opportunistic scheduling that we have described here gain. can also cover cases where there are different constraints from different users. For example, some In general, scheduling gain increases as the number users may have resource requirements while other of users increases. However, the normalized users can have a minimum-data-rate requirement. In scheduling gain (scheduling gain over number of such scenarios, similar optimal solutions can be users) decreases with the increase of the number of provided under this framework using similar users, while the signaling cost per user remains the optimization techniques. same. Hence, it is a question of practical importance to decide the number of users sharing the same 4.1 Precautionary Notes channel. Opportunistic scheduling schemes, as an illustration In summary, opportunistic scheduling presents a new of the cross-layer design of wireless systems, exploit design approach, especially for delay-tolerant data time-varying channel conditions of users with the traffic. It has its own advantages and limitations. It is objective to improve the system throughput. thus important that the system designer to take a However, nothing comes for free. Opportunistic holistic view of the cross-layer design in order to scheduling also has its own costs and limitations avoid potential negative system-wide impacts. discussed as follows. 4.2 Possible Research Directions There are signaling costs involved in all opportunistic scheduling schemes because scheduling decisions Many interesting problems are yet to be resolved in inherently depend on channel. Users need to opportunistic scheduling. We discuss some possible constantly estimate their channel conditions and research problems next. report to the base station. Hence, the actual Short-term Fairness We should note that the scheduling gain should take into account the problem formulations, the objectives, and the signaling costs. constraints are expressed in terms of expectation in Because users need to estimate the channel this paper, which is a long-term performance conditions, estimation errors occur in all scheduling measure. There is no guarantee of short-term schemes. There are various sources of estimation performance. In [10], an extension is provided to errors: errors of estimations of channels, errors of improve short-term performance. The basic idea is to estimations of parameters involved in scheduling increase a user's probability of transmission when it schemes, and errors caused by various delays such as is behind in its share. There is a need for general transmission delay, estimation delay, and restriction short-term fairness criteria tailored to wireless of time-slots, etc. In general, if the variation of networks and dealing with the short-term channel conditions is relatively slow, then the performance in depth. We also refer interested estimation is good. We recommend a rigorous study readers to [5-8] where queueing delays are on this problem, especially in the case of fast fading. considered, [13] where real-time scheduling is discussed, and [27] where user-level performance is Opportunistic scheduling exploits the fluctuation of studied. channel conditions, and thus scheduling gain inherently depends on the amplitude of the variations Delay A problem related to improving short-term performance is to schedule traffic with deadlines, i.e., problems studied here have the net effect of increas- real-time traffic. Specifically, upon arrival, each real- ing the overall effective capacity of the wireless time packet has a delay deadline, and packets that network. This means that the network can now cannot be transmitted before their deadlines are accommodate more users or higher-data-rate users. dropped/marked. Research on scheduling with Thus, we know that keeping all else fixed, the deadlines in the wireline setting has led to various admissible region of the wireless network will approaches. The additional challenge in wireless increase by using opportunistic scheduling schemes. networks is due to the time-varying channel A challenging problem that still remains is how to conditions. Approaches to these problems may make intelligent admission control decisions on include off-line optimal solutions with the whether or not to allow a new user into a cell. assumption of entire traffic and channel information, Although admission control is a difficult problem in on-line model-based solutions, and heuristic/greedy wireless systems whether or not opportunistic algorithms. Heuristic algorithms play an important scheduling is used, it is more challenging in the role in real-time scheduling problems because context of opportunistic scheduling because (typically) the optimal scheduling problem is NP- opportunistic scheduling increases the system complete and simplicity is a desirable feature. In the dynamics. wireline world, it is sometimes the case that Multi-hop Networks Most of the current research on complicated scheduling schemes do not have opportunistic scheduling focuses on the downlink of significant performance gains over simple schemes, a cellular system. In such a system, there exists a such as static priority or earliest-deadline-first. A natural central controller, the base station. An similar situation may be expected to hold for wireless interesting question is whether and how to exploit the networks. time-domain diversity in a distributed multi-hop Another challenging problem is to minimize the environment, such as an ad-hoc network average packet delay. Although many schemes can [15,20,24,28]. stabilize the queues, to control the average delay 5. Conclusion performance is much more challenging. To meet the increasing demand for wireless services, Multi-carrier System Opportunistic scheduling is especially affordable wireless data services, wireless based on the premise that the wireless channel is spectrum efficiency is becoming increasingly im- time-varying, and we can schedule users to transmit portant. In wireless networks, users experience at those times that are opportunistically “relatively unreliable, location-dependent, and time-varying good.” This idea can be extended to the frequency channel conditions. Traditionally, the channel domain: we opportunistically schedule users to variation is considered as a negative factor for frequencies (and time) that are relatively good [19]. reliable communication, and should be mitigated by An example of such systems is an OFDM system. A methods such as time interleaving, power control, concern of opportunistic scheduling in such systems and multiple antennas. On the other hand, is the signaling cost. Because each sub-carrier is very opportunistic scheduling is designed to exploit the narrow in OFDM systems, signaling should be variation of channel conditions to improve spectrum carefully designed to ensure good channel estimation efficiency. It adds an additional degree of freedom to of users on different sub-carriers while avoiding the system: time-domain diversity or also called significant signaling overhead. multi-user diversity. It improves spectrum efficiency, Physical Layer The performance of opportunistic especially for delay-tolerant data transmissions. scheduling schemes is closely related to physical- Various opportunistic scheduling schemes have been layer designs. As explained earlier, estimation errors studied. A common objective is to improve/maximize occur in all opportunistic scheduling schemes. On system performance (e.g., throughput) under various one hand, we need a better understanding of the fairness and QoS constraints. In many cases, the effect of channel estimation errors on scheduling optimal policies are given in a simple parametric schemes. On the other hand, it calls for better channel form, hence lending themselves to easy estimation techniques and smart coding schemes implementations. The advantages of opportunistic (e.g., incremental redundancy transmission schemes scheduling also include the ability to work with other with turbo codes). Further, it is also important to resource management mechanisms. A good example study the performance of opportunistic scheduling in of this is the joint scheduling and power-allocation multiple antenna systems. In summary, a better scheme [23]. In summary, opportunistic scheduling, understanding of physical-layer technologies or even with its own advantages and limitations, is an layer-breaking designs can be potentially beneficial. excellent illustration of cross-layer design. Admission Control The opportunistic scheduling 6. Acknowledgement [15] X. Qin and R. Berry, “Exploiting multiuser diversity This research is supported in part by NSF awards for medium access control in wireless networks,” in ANI-0207728, ANI-0099137, EIA-0130599, ECS- Proceedings of IEEE Infocom 2003. 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