Scheduling (Chapter 9) Outline

Transcription

1 Scheduling (Chapter 9) An Engineering Approach to Computer Networking S. Keshav (Based on slides of S. Keshav and material of J. Liebeherr, J. Crowcroft, ) Outline What is scheduling Requirements of a scheduling discipline Fundamental choices Scheduling best effort connections Scheduling guaranteed-service connections Packet drop strategies

2 Sharing always results in contention Scheduling A scheduling discipline resolves contention: who s next? Key to fairly sharing resources and providing performance guarantees Components. A scheduling discipline does two things: decides service order manages queue of service requests Example: Consider queries awaiting web server. Scheduling discipline decides: des: (a) service order, and (b) if some query should be ignored Where? Anywhere where contention may occur At every layer of protocol stack Usually studied at network layer, at output queues of switches Scheduling in router Input lines: no input buffering Packet classifier: policy based classification Correct output queue: Forwarding / routing tables switching fabric Output buffer (queue) Scheduler: Which output queue serviced next Forwarding/routing policy How to classify packets Constrains on routing and forwarding

3 Traffic management Set of procedures responsible for ensuring that a network operates es efficiently Operates at multiple time scales (packet / Call / Network level) (us) Scheduling and buffer management (ms) Feedback control (sec) Renegotiation (min) Call Admission Control - routing (day +) Capacity planning Network design Complexity depends on: Range of services, Types of users, Desired efficiency What can scheduling disciplines do? Give different users different qualities of service (Enforce QoS at multiplexing point) Scheduling disciplines can allocate (guarantee) bandwidth delay loss delay jitter They also determine how fair the network is Why do we need one? applications need it best-effort effort (adaptive, non-real time) e.g. , some types of file transfer (fairness(-isolation) isolation) is main concern) guaranteed service (non-adaptive, real time) e.g. voice, interactive video (+ fair allocation of excess resources)

4 Conservation Law Consider N flows at a scheduler traffic arrives from flow i at a mean rate? i x i : mean service time for a packet form flow i Mean utilization due to flow i is? i =? i x i Let q i denote the mean waiting time of flow i s packets Conservation law says that if the scheduler is work conserving S i? i q i =constant independent of scheduling discipline We can not give all flows a lower delay than they would get under FCFS If one of the flows is given a lower delay by the scheduler then it must be by increasing the delay for one or more of the others Outline What is scheduling Requirements of a scheduling discipline Fundamental choices Scheduling best effort connections Scheduling guaranteed-service connections Packet drop strategies

5 Requirements An ideal scheduling discipline is easy to implement is fair provides performance bounds allows easy admission control decisions to decide whether a new flow can be allowed Requirements: 1. Ease of implementation Scheduling discipline has to make a decision once every few microseconds! Should be implementable in a few instructions or hardware Work per packet should scale less than linearly with number of active connections Requirements:. Fairness Scheduling discipline allocates a resource An allocation is fair if it satisfies max-min min fairness Intuitively each connection gets no more than what it wants the excess, if any, is equally shared

6 Fairness (contd.) max-min min fairness Intuitively each connection gets no more than what it wants the excess, if any, is equally shared Fairness (contd.) m n M n = min( x n, M ) n 1 C m = i = 1 i N n + 1 : resource available n 1 n N xn : resource demand by flow n x1 x C : capacity of resource M m n n to flow : actual resource allocation n Max-min fair share criteria Flows are allocated resource in order of increasing demand Flows get no more than they need Flows which have not been allocated as much as they demand get an equal share of the available resource to flow n... x N Weighted max-min min fair share possible

7 Fairness (contd.) Example: C=10, four flows with demands of,.6, 4, 5 Actual resource allocations are,.6,.7, M 1 = =.5, x1 = min(,.5) =, M = =.6, x = min(.6,.6) = M 3 = =.7, x3 = min(4,.7) =.7, M 4 = =.7, x4 1 Fairness is intuitively a good idea But it also provides protection = min(5,.7) =.7 Fairness is a global objective, but scheduling is local Each endpoint must restrict its flow to the smallest locally fair allocation along its path Dynamics + delay => global fairness may never be achieved Requirements: 3. Performance bounds What is it? A way to obtain a desired level of service Can be deterministic or statistical Common parameters are bandwidth, delay, delay-jitter, loss Bandwidth Specified as minimum bandwidth measured over a prespecified interval (Meaningless without an interval!) Can be a bound on average rate or peak rate Peak is measured over a small interval Average is asymptote as intervals increase without bound Delay and delay-jitter Bound on some parameter of the delay distribution curve

8 Req ments: 4. Ease of admission control Admission control needed to provide QoS Overloaded resource cannot guarantee performance Choice of scheduling discipline affects ease of admission control algorithm Outline What is scheduling Why we need it Requirements of a scheduling discipline Fundamental choices Scheduling best effort connections Scheduling guaranteed-service connections Packet drop strategies

9 Fundamental choices 1. Number of priority levels. Work-conserving vs. non-work-conserving 3. Degree of aggregation 4. Service order within a level Choices: 1. Priority Packet is served from a given priority level only if no packets exist at higher levels (multilevel priority with exhaustive service) Highest level gets lowest delay Watch out for starvation! Usually map priority levels to delay classes Low bandwidth urgent messages Realtime Non-realtime Priority

10 Choices:. Work conserving vs. non-workconserving Work conserving discipline is never idle when packets await service Why bother with non-work conserving? Makes traffic more predictable Less jitter Less buffer space Non-work-conserving disciplines Key conceptual idea: delay packet till eligible Reduces delay-jitter => fewer buffers in network ( smoothing of flows fewer and smaller bursts) How to choose eligibility time? rate-jitter regulator bounds (maximum) outgoing rate delay-jitter regulator compensates for variable delay at previous hop

11 Regulators Rate-jitter regulator Example: peak rate regulator (assume fixed packet size) E(k) eligibility time for the kth packet, A(k) its arrival time X min =1 / peak rate [sec/packet] E(1)=A(1), E(k+1)=max(E(k)+X min, A(k+1)) Delay jitter regulator E(i,k): eligibility time for the kth packet at the ith switch E(0,k) = A(0,k), E(i+1,k) = E(i,k) + D + L D: delay bound at previous switch L: maximum transmission delay on link (switch i, switch i+1) Example: seven packets arrive, equally spaced, to switch Assume that at each switch: the maximum delay of a packet satisfies a delay bound D propagation delays are negligible 3 The first packet experiences the maximum delay D Subsequent packet arrivals do not experience any queuing delay (such a scenario can occur, if, at each switch, packet 0 is delayed ed by higher priority traffic, and there is no additional higher priority traffic once packet 0 has been transmitted)

12 Example, Work-conserving schedulers max. delay D max. delay D max. delay D Packet arrivals at switch 1 Packet arrivals at switch Packet arrivals at switch 3 Packet departures from switch 3 t o t o +D t o +D t o +3D Example, Rate controlled schedulers t o max. delay D max. delay D max. delay D t o +D t o +D t o +3D Packet arrivals at Switch 1 Packet arrivals to regulator of switch Packet arrivals to Scheduler of switch Packet arrivals to regulator of switch 3 Packet arrivals to Scheduler of switch 3 Packet departures from Switch 3

13 Do we need non-work-conservation? Can remove delay-jitter at an endpoint instead but also reduces size of switch buffers Increases mean delay not a problem for playback applications Wastes bandwidth can serve best-effort effort packets instead Always punishes a misbehaving source can t have it both ways Bottom line: not too bad, implementation cost may be the biggest problem Choices: 3. Degree of aggregation More aggregation less state cheaper smaller VLSI less to advertise BUT: less individualization Solution aggregate to a class, members of class have same performance requirement no protection within class

14 Choices: 4. Service within a priority level In order of arrival (FCFS) or in order of a service tag Service tags => can arbitrarily reorder queue Need to sort queue, which can be expensive FCFS Packets are served in the order they arrive (no packet differentiation) Simple Delay guarantees proportional to buffer size No flow isolation (protection) or bandwidth guarantees Service tags with appropriate choice, both protection and delay bounds possible Summary Two sorts of applications: best effort and guaranteed service Best effort connections require fair service provided by GPS, which is unimplementable emulated by WFQ and its variants Guaranteed service connections require performance guarantees provided by WFQ, but this is expensive may be better to use rate-controlled schedulers

15 Outline What is scheduling Why we need it Requirements of a scheduling discipline Fundamental choices Scheduling best effort connections Scheduling guaranteed-service connections Packet drop strategies Scheduling best-effort connections Main requirement is fairness Achievable using Generalized processor sharing (GPS) [bit-by-bit round robin (BR)] Generalized processor sharing (GPS) Bit-by-bit bit round robin (BR)

16 Generalized Processor Sharing (GPS) the queues contain fluid queue weights f 1, f, f N server empties queues 1. simultaneously. at rates proportional to the weights A queue is backlogged whenever it is non-empty non-backlogged flows get already as much service as they could use backlogged connections share the remaining bandwidth (in proportion to their weights) Let S(i,t,t) t) be the amount of fluid served from queue i in [t, t,t] t] For any queue i that is backlogged during the interval [t, t,t] t] the following holds: S( i, τ, t) φ S( j, τ, t) ϕ i j GPS continued S( i, τ, t) S( j, τ, t) = φ φ holds for any [t 1,t ] during which queues i,j are continuously backlogged i If S(t, t,t) is the total amount of service provided by the server in[t, t,t] S φi ( i, τ, t) N j = 1φ j For fixed rate server with service rate r minimum rate guaranteed to queue i is j S( τ, t) holds for any [t,t] t] during which queue i is continuously backlogged S ( τ, t) = r( t τ ) φi i r = 1φ g N j j

17 GPS Example 3 connections with φ(1) = 0.5 φ() = 0.5 φ(3) = 0.5 During [0,] Session and Session 3 are backlogged. φ() / ( φ() + φ(3) ) = 1/3 φ(3) / ( φ() + φ(3) ) = /3 During [,3] Session 1, Session and Session 3 are backlogged. GPS continued GPS is unimplementable! we cannot serve infinitesimals, only packets No packet discipline can be as fair as GPS while a packet is being served, we are unfair to others Degree of unfairness can be bounded Define: work(i,a,b) = # bits transmitted for connection i in time [a,b] Absolute fairness bound for discipline S Max (work_gps(i,a,b) - work_s(i, a,b)) Relative fairness bound for discipline S Max (work_s(i,a,b) - work_s(j,a,b))

18 Let GPS continued K routers (1 k K) along the path, r(k): service rate of router k that serve N flows (1 i N), f(i,k i,k): weight of flow i at router k g(i,k) minimum guaranteed rate to flow i at router k g(i) minimum guaranteed rate to flow i along the path g(i)=min {g(i,1),, g(i,k)} g( i, k ) = φ ( i, k) r ( k) φ( j, k ) N j = 1 S(.) is the service given to a flow by the GPS emulation G(.) is the service that would be given by GPS AFB = S( i, τ, t) G( i, τ, t) g( i) g( i) RFB = S( i, τ, t) S( j, τ, t) g( i) g( j) What next? We can t implement GPS So, lets see how to emulate it We want to be as fair as possible But also have an efficient implementation

19 Weighted round robin Serve a packet from each non-empty queue in turn Unfair if packets are of different length or weights are not equal Different weights, fixed packet size serve more than one packet per visit, after normalizing to obtain integer weights Different weights, variable size packets normalize weights by mean packet size e.g. weights {0.5, 0.75, 1.0}, mean packet sizes {50, 500, 1500} normalize weights: {0.5/50, 0.75/500, 1.0/1500} = { 0.01, , }, normalize again {60, 9, 4} Weighted round robin (example) φ(1) =, Packet Size(1)=50 bytes, φ() = 1, Packet Size()=100 bytes normalized weights (by mean packet size) : φ(1) / Packet Size(1) = 0.04 bytes -1 normalized weights: φ(1) = 4 φ() = 1 φ() / Packet Size()=0.01 bytes -1 Not fair in time scales shorter than a round

20 Problems with Weighted Round Robin With variable size packets and different weights, need to know mean packet size in advance In practice this might be unpredictable (Ex: compressed video) Can be unfair for long periods of time E.g. T3 trunk with 500 connections, each connection has mean packet length 500 bytes, 50 with weight 1, 50 with weight 10 Each packet takes 500 * 8/45 Mbps = 88.8 microseconds Round time =750 * 88.8 = 44. ms Potentially unfair for short lived flows / flows with small weights / if there is a large number of flows Deficit Round Robin Modifies WRR to handle variable packet sizes without knowing the mean packet size of each connection in advance. Idea: Associate each queue with a deficit counter C. (initialized to 0). At each round: If the queue is not empty C= C+quantum size. else (the queue is empty) C = 0. If C packet size then serve the packet at the head of the queue, C = C-packet size. Easy to implement. Like WRR unfair at time scales smaller than a frame time.

21 Deficit Round Robin Example Quantum Size = (Assuming φ(1) = φ() = φ(3) (3)) Weighted Fair Queuing(WFQ)<=>Packet-by-packet GPS(PGPS) Deals better with variable size packets and weights GPS is fairest discipline Find the finish time of a packet, had we been doing GPS Then serve packets in order of their finish times Properties of PGPS Packet finish transmission times in PGPS are at most one maximum size packet later than GPS Queue sizes in PGPS is at most one maximum size packet larger than in GPS if GPS has served x bits from connection A by time t PGPS would have served at least x - P bits, where P is the largest possible packet in the network

22 Example packet lenghts: 3,, 1 weights: f 1 = f = f 3 arrivals: t=0, t=1, t=3 GPS t PGPS t Example packet lenghts: 3,, 1/3 weights: f 1 = f = f 3 arrivals: t=0, t=1, t=4 The next packet to depart has not arrived GPS t PGPS t

23 WFQ: first cut Suppose, in each round, the server served one bit from each active connection Round number is the number of rounds already completed can be fractional If a packet of length p arrives to an empty queue when the round number is R,, it will complete service when the round number is R + p => finish number is R + p independent of the number of other connections! If a packet arrives to a non-empty queue, and the previous packet has a finish number of f,, then the packet s finish number is f+p Serve packets in order of finish numbers A catch A queue may need to be considered non-empty even if it has no packets in it e.g. packets of length 1 from connections A and B, on a link of speed 1 bit/sec at time 1, packet from A served, round number = 0.5 A has no packets in its queue, yet should be considered non- empty, because a packet arriving to it at time 1 should have finish number 1+ p A connection is active if the last packet served from it, or in its queue, has a finish number greater than the current round number

24 WFQ continued To sum up, assuming we know the current round number R Finish number of packet of length p if arriving to active connection = previous finish number + p if arriving to an inactive connection = R + p (How should we deal with weights?) To implement, we need to know two things: is connection active? if not, what is the current round number? Answer to both questions depends on computing the current round number (why?) WFQ: computing the round number Naively: round number = number of rounds of service completed so far what if a server has not served all connections in a round? what if new conversations join in halfway through a round? Redefine round number as a real-valued variable that increases at a rate inversely proportional to the number of currently active connections this takes care of both problems With this change, WFQ emulates GPS instead of bit-by-bit RR

25 WFQ: finish number When a packet arrives, the scheduler computes the finish number of the packet F(i,k,t) = max { F(i,k-1,t), R(t) } + P(i,k,t) / f(i) F(i,k-1,t): finish number of the k-1th packet on connection i P(i,k,t): size of k-th packet arriving on connection i at time t f(i): weight of connection i R(t): round number R t) / t = r / ϕ(i) ( i active r: link capacity A connection is active if the last packet served from it, or in its queue, has a finish number greater than the current round number link service rate = 1unit / s Compute: Example the finish number of all the packets the round number when the system becomes idle 1 GPS t 1 PGPS t

26 Example /3 1/ 1/3 1 1 GPS t 1 PGPS t WFQ implementation On packet arrival: use source + destination address (or VCI) to classify it and look up finish number of last packet served (or waiting to be served) recompute round number compute finish number insert in priority queue sorted by finish numbers if no space, drop the packet with largest finish number On service completion select the packet with the lowest finish number

27 Relation between WFQ (PGPS) and GPS In GPS, a packet completes service when the round number increases beyond the packet s finish number The finish time for a packet in WFQ is not the same as its finish number Once assigned, the finish number does not depend on future packet arrivals and departures The finish number of a packet is independent of the other connections awaiting service, because the rate of increase of the round number varies with the number of active connections Problem: iterated deletion Round number # active conversations A sever recomputes round number on each packet arrival At any recomputation, the number of conversations can go up at most by one, but can go down to zero => overestimation Trick use previous count to compute round number if this makes some conversation inactive, recompute repeat until no conversations become inactive

28 A Example A B 100 GPS t B 100 PGPS t / Analysis Unweighted case: if GPS has served x bits from connection A by time t WFQ would have served at least x - P bits, where P is the largest possible packet in the network WFQ could send more than GPS would => absolute fairness bound > P To reduce bound, choose smallest finish number only among packets that have started service in the corresponding GPS system (WF Q) requires a regulator to determine eligible packets

29 Evaluation Pros like GPS, it provides protection can obtain worst-case end-to-end delay bound gives users incentive to use intelligent flow control (and also provides rate information implicitly) Cons needs per-connection state iterated deletion is complicated requires a priority queue Self-Clocked Fair Queuing (SCFQ) Variant of WFQ Avoids the need to compute R(t) by using in its place, the label of the packet currently in service. F(i,k) = max {F(i,k-1), CF} + P(i,k) / f(i) CF: finish number of the current packet in service O(1) complexity of virtual time update Is easier to implement than WFQ can be unfair over short time scales

30 Start time Fair Queuing (SFQ) Better worst case delays than SCFQ Start tag: S(i,k) = max {F(i,k-1),CR} CR: start number of the current packet in service If there are no more packets, CR is set to the largest of the finish numbers of any packet sent so far. Finish tag : F(i,k) = S(i,k) + P(i,k) / f i Outline What is scheduling Why we need it Requirements of a scheduling discipline Fundamental choices Scheduling best effort connections Scheduling guaranteed-service connections Packet drop strategies

31 Scheduling guaranteed-service connections With best-effort effort connections, goal is fairness With guaranteed-service connections what performance guarantees are achievable? how easy is admission control? We now study some scheduling disciplines that provide performance guarantees WFQ Turns out that WFQ also provides performance guarantees Bandwidth bound ratio of weights * link capacity e.g. connections with weights 1,, 7; link capacity 10 connections get at least 1,, 7 units of b/w each End-to-end delay bound assumes that the connection doesn t send too much (otherwise its packets will be stuck in queues) more precisely, connection i should be leaky-bucket regulated # bits sent in time [t 1, t ] <=? i (t - t 1 ) + s i

32 Parekh-Gallager theorem Let a connection be allocated weights at each WFQ scheduler along its path, so that the least bandwidth it is allocated is g(i) Let it be leaky-bucket regulated such that # bits sent in time [t 1, t ] <=? i (t - t 1 ) + s i Let the connection pass through K schedulers, where the kth scheduler has a rate r(k) Let the largest packet allowed in the network be P max end _ to _ end _ delay σ i / g ( i) + K 1 k = 1 P K / g( i, k ) + i P / r ( k ) max, max k = 1 Significance Theorem shows that WFQ can provide end-to-end delay bounds So WFQ provides both fairness and performance guarantees Boud holds regardless of cross traffic behavior Can be generalized for networks where schedulers are variants of WFQ, and the link service rate changes over time

33 Problems To get a delay bound, need to pick g the lower the delay bounds, the larger g needs to be large g => exclusion of more competitors from link g can be very large, in some cases 80 times the peak rate! Sources must be leaky-bucket regulated but choosing leaky-bucket parameters is problematic WFQ couples delay and bandwidth allocations low delay requires allocating more bandwidth wastes bandwidth for low-bandwidth low-delay sources Earliest Due Date Assign each packet a deadline packets served in order of their deadlines Packets assigned deadlines closer to their arrival times receive a lower delay bound than packets assigned farther deadlines

34 Delay-Earliest Due Date Delay-EDD prescribes how to assign deadlines to packets A source is required to send slower than its peak rate Bandwidth at scheduler reserved at peak rate Deadline = expected arrival time + delay bound If a source sends faster than contract, delay bound will not apply Each packet gets a hard delay bound Delay bound is independent of bandwidth requirement but reservation is at a connection s peak rate Implementation requires per-connection state and a priority queue Rate-controlled scheduling A class of disciplines two components: regulator and scheduler incoming packets are placed in regulator where they wait to become eligible then they are put in the scheduler Regulator shapes the traffic, scheduler provides performance guarantees

35 Examples Recall rate-jitter regulator bounds maximum outgoing rate delay-jitter regulator compensates for variable delay at previous hop Rate-jitter regulator + FIFO similar to Delay-EDD (what is the difference?) Rate-jitter regulator + multi-priority FIFO gives both bandwidth and delay guarantees (RCSP) Delay-jitter regulator + EDD gives bandwidth, delay,and delay-jitter bounds (Jitter-EDD) Analysis First regulator on path monitors and regulates traffic => bandwidth dth bound End-to-end delay bound delay-jitter regulator reconstructs traffic => end-to-end delay is fixed (= worst-case delay at each hop) rate-jitter regulator partially reconstructs traffic can show that end-to-end delay bound is smaller than (sum of delay bound at each hop + delay at first hop)

36 Decoupling Can give a low-bandwidth connection a low delay without overbooking E.g consider connection A with rate 64 Kbps sent to a router with rate- jitter regulation and multipriority FCFS scheduling After sending a packet of length l,, next packet is eligible at time (now + l/64 Kbps) If placed at highest-priority queue, all packets from A get low delay Can decouple delay and bandwidth bounds, unlike WFQ Evaluation Pros flexibility: ability to emulate other disciplines can decouple bandwidth and delay assignments end-to-end delay bounds are easily computed do not require complicated schedulers to guarantee protection can provide delay-jitter bounds Cons require an additional regulator at each output port delay-jitter bounds at the expense of increasing mean delay delay-jitter regulation is expensive (clock synch, timestamps)

37 Summary Two sorts of applications: best effort and guaranteed service Best effort connections require fair service provided by GPS, which is unimplementable emulated by WFQ and its variants Guaranteed service connections require performance guarantees provided by WFQ, but this is expensive may be better to use rate-controlled schedulers Outline What is scheduling Why we need it Requirements of a scheduling discipline Fundamental choices Scheduling best effort connections Scheduling guaranteed-service connections Packet drop strategies

38 Packet dropping Packets that cannot be served immediately are buffered Full buffers => packet drop strategy Packet losses happen almost always from best-effort effort connections (why?) Shouldn t drop packets unless imperative packet drop wastes resources (why?) Classification of drop strategies 1. Degree of aggregation. Drop priorities 3. Early or late 4. Drop position

39 1. Degree of aggregation Degree of discrimination in selecting a packet to drop E.g. in vanilla FIFO, all packets are in the same class Instead, can classify packets and drop packets selectively The finer the classification the better the protection Max-min fair allocation of buffers to classes drop packet from class with the longest queue (why?). Drop priorities Drop lower-priority packets first How to choose? endpoint marks packets regulator marks packets congestion loss priority (CLP) bit in packet header CLP bit: pros and cons Pros if network has spare capacity, all traffic is carried during congestion, load is automatically shed Cons separating priorities within a single connection is hard what prevents all packets being marked as high priority?

40 . Drop priority (contd.) Special case of AAL5 want to drop an entire frame, not individual cells cells belonging to the selected frame are preferentially dropped Drop packets from nearby hosts first because they have used the least network resources can t do it on Internet because hop count (TTL) decreases 3. Early vs. late drop Early drop => drop even if space is available signals endpoints to reduce rate cooperative sources get lower overall delays, uncooperative sources get severe packet loss Early random drop drop arriving packet with fixed drop probability if queue length exceeds threshold intuition: misbehaving sources more likely to send packets and see packet losses doesn t work!

41 3. Early vs. late drop: RED Random early detection (RED) makes three improvements Metric is moving average of queue lengths small bursts pass through unharmed only affects sustained overloads Packet drop probability is a function of mean queue length prevents severe reaction to mild overload Can mark packets instead of dropping them allows sources to detect network state without losses RED improves performance of a network of cooperating TCP sources No bias against bursty sources Controls queue length regardless of endpoint cooperation 4. Drop position Can drop a packet from head, tail, or random position in the queue Tail easy default approach Head harder lets source detect loss earlier

42 4. Drop position (contd.) Random hardest if no aggregation, hurts hogs most unlikely to make it to real routers Drop entire longest queue easy almost as effective as drop tail from longest queue