CS60002 Distributed Systems
Text Book: • “Advanced Concepts in Operating Systems” by Mukesh Singhal and Niranjan G. Shivaratri will cover about half the course, supplemented by copies of papers
Xerox, notes, copies of papers etc. will cover the rest.
Text Book: • “Advanced Concepts in Operating Systems” by Mukesh Singhal and Niranjan G. Shivaratri will cover about half the course, supplemented by copies of papers
Xerox, notes, copies of papers etc. will cover the rest.
What is a distributed system? A very broad definition: A set of autonomous processes communicating among themselves to perform a task Autonomous: able to act independently Communication: shared memory or message passing “Concurrent system” : a better term probably
A more restricted definition: • A network of autonomous computers that communicate by message passing to perform some task A practical “distributed system” will probably have both – Computers that communicate by messages – Processes/threads on a computer that communicate by messages or shared memory
Advantages • Resource Sharing • Higher Performance • Fault Tolerance • Scalability
Why is it hard to design them? The usual problem of concurrent systems: – Arbitrary interleaving of actions makes the system hard to verify Plus • No globally shared memory (therefore hard to collect global state) • No global clock • Unpredictable communication delays
Models for Distributed Algorithms – Topology : completely connected, ring, tree etc. – Communication : shared memory/message passing (reliable? Delay? FIFO/Causal? Broadcast/multicast?) – Synchronous/asynchronous – Failure models (fail stop, crash, omission, Byzantine…) An algorithm need to specify the model on which it is supposed to work
Complexity Measures • Message complexity : no. of messages • Communication complexity/Bit Complexity : no. of bits • Time complexity : For synchronous systems, no. of rounds. For asynchronous systems, different definitions are there.
Some Fundamental Problems • Ordering events in the absence of a global clock • Capturing the global state • Mutual exclusion • Leader election • Clock synchronization • Termination detection • Constructing spanning trees • Agreement protocols
Ordering of Events and Logical Clocks
Ordering of Events Lamport’s Happened Before relationship: For two events a and b, a → b if
a and b are events in the same process and a occurred before b
a is a send event of a message m and b is the corresponding receive event at the destination process
a → c and c → b for some event c
a → b implies a is a potential cause of b Causal ordering : potential dependencies “Happened Before” relationship causally orders events • If a → b, then a causally affects b • If a → b and b → a, then a and b are concurrent ( a || b)
Logical Clock Each process i keeps a clock Ci. • Each event a in i is timestamped C(a), the value of Ci when a occured • Ci is incremented by 1 for each event in i • In addition, if a is a send of message m from process i to j, then on receive of m, C j = max(C j, C(a)+1)
Points to note: • if a → b, then C(a) < C(b) • → is an irreflexive partial order • Total ordering possible by arbitrarily ordering concurrent events by process numbers
Limitation of Lamport’s Clock a → b implies C(a) < C(b) BUT C(a) < C(b) doesn’t imply a → b !! So not a true clock !!
Solution: Vector Clocks
Ci is a vector of size n (no. of processes) C(a) is similarly a vector of size n Update rules: • Ci[i]++ for every event at process i • if a is send of message m from i to j with vector timestamp tm, on receive of m: C j[k] = max(C j[k], tm[k]) for all k
For events a and b with vector timestamps ta and tb, • ta = tb iff for all i, ta[i] = tb[i] • ta ≠ tb iff for some i, ta[i] ≠ tb[i] • ta ≤ tb iff for all i, ta[i] ≤ tb[i] • ta < tb iff (ta ≤ tb and ta ≠ tb) • ta || tb iff (ta < tb and tb < ta)
• a → b iff ta < tb • Events a and b are causally related iff ta < tb or tb < ta, else they are concurrent • Note that this is still not a total order
Causal ordering of messages: application of vector clocks
• If send(m1)→ send(m2), then every recipient of both message m1 and m2 must “deliver” m1 before m2. “deliver” – when the message is actually given to the application for processing
Birman-Schiper-Stephenson Protocol • To broadcast m from process i, increment Ci(i), and timestamp m with VTm = Ci[i] • When j ≠ i receives m, j delays delivery of m until – C j[i] = VTm[i] –1 and – C j[k] ≥ VTm[k] for all k ≠ i – Delayed messaged are queued in j sorted by vector time. Concurrent messages are sorted by receive time.
• When m is delivered at j, C j is updated according to vector clock rule.
Problem of Vector Clock
• message size increases since each message needs to be tagged with the vector • size can be reduced in some cases by only sending values that have changed
Capturing Global State
Global State Collection Applications: – Checking “stable” properties, checkpoint & recovery Issues: – Need to capture both node and channel states – system cannot be stopped – no global clock
Some notations: – LSi : local state of process i – send(mij) : send event of message mij from process i to process j – rec(mij) : similar, receive instead of send – time(x) : time at which state x was recorded – time (send(m)) : time at which send(m) occured
send(mij) є LSi iff time(send(mij)) < time(LSi) rec(mij) є LS j iff time(rec(mij)) < time(LS j) transit(LSi,LS j) = { mij | send(mij) є LSi and rec(mij) є LS j} inconsistent(LSi, LS j) = {mij | send(mij) є LSi and rec(mij) є LS j}
Global state: collection of local states GS = {LS1, LS2,…, LSn} GS is consistent iff for all i, j, 1 ≤ i, j ≤ n, inconsistent(LSi, LS j) = Ф GS is transitless iff for all i, j, 1 ≤ i, j ≤ n, transit(LSi, LS j) = Ф GS is strongly consistent if it is consistent and transitless.
Chandy-Lamport’s Algorithm • Uses special marker messages. • One process acts as initiator, starts the state collection by following the marker sending rule below. • Marker sending rule for process P: – P records its state; then for each outgoing channel C from P on which a marker has not been sent already, P sends a marker along C before any further message is sent on C
• When Q receives a marker along a channel C: – If Q has not recorded its state then Q records the state of C as empty; Q then follows the marker sending rule – If Q has already recorded its state, it records the state of C as the sequence of messages received along C after Q’s state was recorded and before Q received the marker along C
Points to Note: • Markers sent on a channel distinguish messages sent on the channel before the sender recorded its states and the messages sent after the sender recorded its state • The state collected may not be any state that actually happened in reality, rather a state that “could have” happened • Requires FIFO channels • Network should be strongly connected (works obviously for connected, undirected also) • Message complexity O(|E|), where E = no. of links
Lai and Young’s Algorithm • Similar to Chandy-Lamport’s, but does not require FIFO • Boolean value X at each node, False indicates state is not recorded yet, True indicates recorded • Value of X piggybacked with every application message • Value of X distinguishes presnapshot and post-snapshot messages, similar to the Marker
Mutual Exclusion
Mutual Exclusion • very well-understood in shared memory systems • Requirements: – at most one process in critical section (safety) – if more than one requesting process, someone enters (liveness) – a requesting process enters within a finite time (no starvation) – requests are granted in order (fairness)
Classification of Distributed Mutual Exclusion Algorithms • Non-token based/Permission based – Permission from all processes: e.g. Lamport, Ricart-Agarwala, Raicourol-Carvalho etc. – Permission from a subset: ex. Maekawa • Token based – ex. Suzuki-Kasami
Some Complexity Measures
• No. of messages/critical section entry • Synchronization delay • Response time • Throughput
Lamport’s Algorithm • Every node i has a request queue qi, keeps requests sorted by logical timestamps (total ordering enforced by including process id in the timestamps) To request critical section: – send timestamped REQUEST (tsi, i) to all other nodes – put (tsi, i) in its own queue On receiving a request (tsi, i): – send timestamped REPLY to the requesting node i – put request (tsi, i) in the queue
To enter critical section: – i enters critical section if (tsi, i) is at the top if its own queue, and i has received a message (any message) with timestamp larger than (tsi, i) from ALL other nodes. To release critical section: – i removes it request from its own queue and sends a timestamped RELEASE message to all other nodes – On receiving a RELEASE message from i, i’s request is removed from the local request queue
Some points to note: • Purpose of REPLY messages from node i to j is to ensure that j knows of all requests of i prior to sending the REPLY (and therefore, possibly any request of i with timestamp lower than j’s request) • Requires FIFO channels. • 3(n – 1 ) messages per critical section invocation • Synchronization delay = max. message transmission time • requests are granted in order of increasing timestamps
Ricart-Agarwala Algorithm • Improvement over Lamport’s • Main Idea: – node j need not send a REPLY to node i if j has a request with timestamp lower than the request of i (since i cannot enter before j anyway in this case) • Does not require FIFO • 2(n – 1) messages per critical section invocation • Synchronization delay = max. message transmission time • requests granted in order of increasing timestamps
To request critical section: – send timestamped REQUEST message (tsi, i) On receiving request (tsi, i) at j: – send REPLY to i if j is neither requesting nor executing critical section or if j is requesting and i’s request timestamp is smaller than j’s request timestamp. Otherwise, defer the request. To enter critical section: – i enters critical section on receiving REPLY from all nodes To release critical section: – send REPLY to all deferred requests
Roucairol-Carvalho Algorithm • Improvement over Ricart-Agarwala • Main idea – once i has received a REPLY from j, it does not need to send a REQUEST to j again unless it sends a REPLY to j (in response to a REQUEST from j) – no. of messages required varies between 0 and 2(n – 1) depending on request pattern – worst case message complexity still the same
Maekawa’s Algorithm • Permission obtained from only a subset of other processes, called the Request Set (or Quorum) • Separate Request Set Ri for each process i • Requirements: – for all i, j: Ri ∩ R j ≠ Φ – for all i: i Є Ri – for all i: |Ri| = K, for some K – any node i is contained in exactly D Request Sets, for some D • K = D = sqrt(N) for Maekawa’s
A simple version
To request critical section: – i sends REQUEST message to all process in Ri On receiving a REQUEST message: – send a REPLY message if no REPLY message has been sent since the last RELEASE message is received. Update status to indicate that a REPLY has been sent. Otherwise, queue up the REQUEST To enter critical section: – i enters critical section after receiving REPLY from all nodes in Ri
To release critical section: – send RELEASE message to all nodes in Ri – On receiving a RELEASE message, send REPLY to next node in queue and delete the node from the queue. If queue is empty, update status to indicate no REPLY message has been sent.
• Message Complexity: 3*sqrt(N) • Synchronization delay = 2 *(max message transmission time) • Major problem: DEADLOCK possible • Need three more types of messages (FAILED, INQUIRE, YIELD) to handle deadlock. Message complexity can be 5*sqrt(N) • Building the request sets?
Token based Algorithms • Single token circulates, enter CS when token is present • No FIFO required • Mutual exclusion obvious • Algorithms differ in how to find and get the token • Uses sequence numbers rather than timestamps to differentiate between old and current requests
Suzuki Kasami Algorithm • Broadcast a request for the token • Process with the token sends it to the requestor if it does not need it Issues:
– Current vs. outdated requests – determining sites with pending requests – deciding which site to give the token to
• The token: – Queue (FIFO) Q of requesting processes – LN[1..n] : sequence number of request that j executed most recently • The request message: – REQUEST(i, k): request th message from node i for its k critical section execution • Other data structures – RNi[1..n] for each node i, where RNi[j] is the largest sequence number received so far by i in a REQUEST message from j.
To request critical section: – If i does not have token, increment RNi[i] and send REQUEST(i, RNi[i]) to all nodes – if i has token already, enter critical section if the token is idle (no pending requests), else follow rule to release critical section On receiving REQUEST(i, sn) fat j: – set RN j[i] = max(RN j[i], sn) – if j has the token and the token is idle, send it to i if RN j[i] = LN[i] + 1. If token is not idle, follow rule to release critical section
To enter critical section: – enter CS if token is present To release critical section: – set LN[i] = RNi[i] – For every node j which is not in Q (in token), add node j to Q if RNi[ j ] = LN[ j ] + 1 – If Q is non empty after the above, delete first node from Q and send the token to that node
Points to note:
– No. of messages: 0 if node holds the token already, n otherwise – Synchronization delay: 0 (node has the token) or max. message delay (token is elsewhere) – No starvation
Raymond’s Algorithm • Forms a directed tree (logical) with the token-holder as root • Each node has variable “Holder” that points to its parent on the path to the root. Root’s Holder variable points to itself • Each node i has a FIFO request queue Qi
• To request critical section: – Send REQUEST to parent on the tree, provided i does not hold the token currently and Qi is empty. Then place request in Qi • When a non-root node j receives a request from i – place request in Q j – send REQUEST to parent if no previous REQUEST sent
• When the root receives a REQUEST: – send the token to the requesting node – set Holder variable to point to that node • When a node receives the token: – delete first entry from the queue – send token to that node – set Holder variable to point to that node – if queue is non-empty, send a REQUEST message to the parent (node pointed at by Holder variable)
• To execute critical section: – enter if token is received and own entry is at the top of the queue; delete the entry from the queue • To release critical section – if queue is non-empty, delete first entry from the queue, send token to that node and make Holder variable point to that node – If queue is still non-empty, send a REQUEST message to the parent (node pointed at by Holder variable)
Points to note: • Avg. message complexity O(log n) • Sync. delay (T log n)/2, where T = max. message delay
Leader Election
Leader Election in Rings • Models – Synchronous or Asynchronous – Anonymous (no unique id) or Non-anonymous (unique ids) – Uniform (no knowledge of ‘n’, the number of processes) or non-uniform (knows ‘n’)
• Known Impossibility Result: – There is no Synchronous, nonuniform leader election protocol for anonymous rings – Implications ??
Election in Asynchronous Rings Lelann-Chang-Robert’s Algorithm – send own id to node on left – if an id received from right, forward id to left node only if received id greater than own id, else ignore – if own id received, declares itself “leader”
• works on unidirectional rings • message complexity = θ(n^2)
• Hirschberg-Sinclair Algorithm – operates in phases, requires bidirectional ring – In k th phase, send own id to 2^k processes on both sides of yourself (directly send only to next processes with id and k in it) – if id received, forward if received id greater than own id , else ignore – last process in the chain sends a reply to originator if its id less than received id – replies are always forwarded – A process goes to (k +1)th phase only if it receives a reply from both sides in k th phase – process receiving its own id – declare itself “leader”
• Message Complexity: O(nlgn) • Lots of other algorithms exist for rings • Lower Bound Result: – Any comparison-based leader election algorithm in a ring requires Ώ(nlgn) messages – What if not comparison-based?
Leader Election in Arbitrary Networks • FloodMax – synchronous, round-based – at each round, each process sends the max. id seen so far (not necessarily its own) to all its neighbors – after diameter no. of rounds, if max. id seen = own id, declares itself leader – Complexity = O(d.m), where d = diameter of the network, m = no. of edges – does not extend to asynchronous model trivially • Variations of building different types of spanning trees with no pre-specified roots. Chosen root at the end is the leader (Ex., the DFS spanning tree algorithm we covered earlier)
Clock Synchronization
Clock Synchronization • Multiple machines with physical clocks. How can we keep them more or less synchronized? • Internal vs. External synchronization • Perfect synchronization not possible because of communication delays • Even synchronization within a bound can not be guaranteed with certainty because of unpredictability of communication delays. • But still useful !! Ex. – Kerberos, GPS
How clocks work • Computer clocks are crystals that oscillate at a certain frequency • Every H oscillations, the timer chip interrupts once (clock tick). No. of interrupts per second is typically 18.2, 50, 60, 100; can be higher, settable in some cases • The interrupt handler increments a counter that keeps track of no. of ticks from a reference in the past (epoch) • Knowing no. of ticks per second, we can calculate year, month, day, time of day etc.
Clock Drift • Unfortunately, period of crystal oscillation varies slightly • If it oscillates faster, more ticks per real second, so clock runs faster; similar for slower clocks • For machine p, when correct reference time is t, let machine clock show time as C = C p(t) • Ideally, C p(t) = t for all p, t • In practice, 1 – ρ ≤ dC/dt ≤ 1 + ρ • ρ = max. clock drift rate, usually around 10-5 for cheap oscillators • Drift => Skew between clocks (difference in clock values of two machines)
Resynchronization • Periodic resynchronization needed to offset skew • If two clocks are drifting in opposite directions, max. skew after time t is 2ρt • If application requires that clock skew < δ, then resynchronization period r < δ /(2 ρ) • Usually ρ and δ are known
Cristian’s Algorithm • One m/c acts as the time server • Each m/c sends a message periodically (within resync. period r) asking for current time • Time server replies with its time • Sender sets its clock to the reply • Problems: – message delay – time server time is less than sender’s current time
• Handling message delay: try to estimate the time the message with the timer server’s time took to each the sender – measure round trip time and halve it – make multiple measurements of round trip time, discard too high values, take average of rest – make multiple measurements and take minimum – use knowledge of processing time at server if known • Handling fast clocks – do not set clock backwards; slow it down over a period of time to bring in tune with server’s clock
Berkeley Algorithm • Centralized as in Cristian’s, but the time server is active • time server asks for time of other m/cs at periodic intervals • time server averages the times and sends the new time to m/cs • M/cs sets their time (advances immediately or slows down slowly) to the new time • Estimation of transmission delay as before
External Synchronization • Clocks must be synchronized with real time • Cristian’s algorithm can be used if the time server is synchronized with real time somehow • Berkeley algorithm cannot be used • But what is “real time” anyway?
Measurement of time • Astronomical – traditionally used – based on earth’s rotation around its axis and around the sun – solar day : interval between two consecutive transits of the sun – solar second : 1/86,400 of a solar day – period of earth’s rotation varies, so solar second is not stable – mean solar second : average length of large no of solar days, then divide by 86,400
• Atomic – based on the transitions of Cesium 133 atom – 1 sec. = time for 9,192,631,770 transitions – about 50+ labs maintain Cesium clock – International Atomic Time (TAI) : mean no. of ticks of the clocks since Jan 1, 1958 – highly stable – But slightly off-sync with mean solar day (since solar day is getting longer) – A leap second inserted approx. occasionally to bring it in sync. (so far 32, all positive) – Resulting clock is called UTC – Universal Coordinated Time
• UTC time is broadcast from different sources around the world, ex. – National Institute of Standards & Technology (NIST) – runs radio stations, most famous being WWV, anyone with a proper receiver can tune in – United States Naval Observatory (USNO) – supplies time to all defense sources, among others – National Physical Laboratory in UK – GPS satellites – Many others
NTP : Network Time Protocol • Protocol for time sync. in the internet • Hierarchical architecture – primary time servers (stratum 1) synchronize to national time standards via radio, satelite etc. – secondary servers and clients (stratum 2, 3,…) synchronize to primary servers in a hierrachical manner (stratum 2 servers sync. with stratum 1, startum 3 with stratum 2 etc.).
• Reliability ensured by redundant servers • Communication by multicast (usually within LAN servers), symmetric (usually within multiple geographically close servers), or client server (to higher stratum servers) • Complex algorithms to combine and filter times • Sync. possible to within tens of milliseconds for most machines • But, just a best-effort service, no guarantees • RFC 1305 and www.eecis.udel.edu/~ntp/ for more details
Termination Detection
Termination Detection Model – processes can be active or idle – only active processes send messages – idle process can become active on receiving an computation message – active process can become idle at any time – termination: all processes are idle and no computation message are in transit – Can use global snapshot to detect termination also
Huang’s Algorithm • One controlling agent, has weight 1 initially • All other processes are idle initially and has weight 0 • Computation starts when controlling agent sends a computation message to a process • An idle process becomes active on receiving a computation message • B(DW) – computation message with weight DW. Can be sent only by the controlling agent or an active process • C(DW) – control message with weight DW, sent by active processes to controlling agent when they are about to become idle
Let current weight at process = W 3. Send of B(DW): • •
Find W1, W2 such that W1 > 0, W2 > 0, W1 + W2 = W Set W = W1 and send B(W2)
4. Receive of B(DW): • •
W += DW; if idle, become active
5. Send of C(DW): • •
send C(W) to controlling agent Become idle
6. Receive of C(DW): • •
W += DW if W = 1, declare “termination”
Building Spanning Trees
Building Spanning Trees Applications: • Broadcast • Convergecast • Leader election Two variations: • from a given root r • root is not given a-priori
Flooding Algorithm – starts from a given root r – r initiates by sending message M to all neighbours, sets its own parent to nil – For all other nodes, on receiving M from i for the first time, set parent to i and send M to all neighbors except i. Ignore any M received after that – Tree built is an arbitrary spanning tree – Message complexity = 2m – (n -1) where m = no of edges – Time complexity ??
Constructing a DFS tree with given root • plain parallelization of the sequential algorithm by introducing synchronization • each node i has a set unexplored , initially contains all neighbors of i • A node i (initiated by the root) considers nodes in unexplored one by one, sending a neighbor j a message M and then waiting for a response ( parent or reject ) before considering the next node in unexplored • if j has already received M from some other node, j sends a reject to i
• else, j sets i as its parent, and considers nodes in its unexplored set one by one • j will send a parent message to i only when it has considered all nodes in its unexplored set • i then considers the next node in its unexplored set • Algorithm terminates when root has received parent or reject message from all its neighbours • Worst case no. of messages = 4m • Time complexity O(m)
What if no root given? Main idea: – Nodes have unique ids – A node starts building the DFS tree with itself as root (a single node fragment) spontaneously as in the previous case – Fragments of the spanning tree gets built in parallel, all nodes in each fragment is identified by the id of its root – M carries the fragment id of the sender
– when M sent from node in lower id fragment to node in higher id fragment, lower id fragment is stalled by higher id fragment by not giving a response – When M sent from higher to lower id fragment, node in lower id fragment switches parent to node in higher id tree, resets unexplored, and starts DFS again – Eventually, the highest id node becomes the root (leader election!!) – Message complexity O(mn) !! – Time complexity O(m)
What about MSTs?? Gallager-Humblet-Spira Algorithm
– much more complex! but similar to Kruskal’s – no root given, edge weights assumed to be distinct – MST built up in fragments (subtree of MST) – initially each node in its own fragment – fragments merge, finally just one fragment – outgoing edge – edge that goes between two fragments – known result – min. wt. outgoing edge of a fragment always in MST
Issues: 1. How does a node find its min. wt. outgoing edge? 2. How does a fragment finds its min. wt. outgoing edge? 3. When does two fragments merge? 4. How does two fragments merge?
Some definitions • Each node has three states – Sleeping – initial state – Find – currently finding the fragment’s min. wt. outgoing edge – Found – found the min. wt. outgoing edge • Each fragment has a level – initially, each node is in a fragment of level 0
Merging rule for fragments • Suppose F is a fragment with id X, level L, and min. wt. outgoing edge e. Let fragment at other end of e be F1, with id X1 and level L1. Then – if L < L1, F merges into F1, new fragment has id X1, level L1 – if L=L1, and e is also the min. wt. outgoing edge for F1, then F and F1 merges; new fragment has id X2 = weight of e, and level L + 1; e is called the core edge – otherwise, F waits until one of the above becomes true
How to find min. wt. outgoing edge of a fragment • nodes on core edge broadcasts initiate message to all fragment nodes along fragment edges; contains level and id • on receiving initiate, a node find its min. wt. outgoing edge (in Find state) – how? • nodes send Report message with min. wt. edge up towards the core edge along fragment edges (and enters Found state) • leafs send their min. wt. outgoing edge, intermediate nodes send the min. of their min. wt. outgoing edge and min. edge sent by children in fragment; path info to best edge kept • when Report reaches the nodes on the core edge, min. wt. outgoing edge of the fragment is known.
What then??? • nodes on core edges send Change_core message to node i with min. wt. outgoing edge • node i then sends a Connect message to node j at other end with its level • If j’s fragment level is greater than i’s, initiate message sent from j to i. This updates level and id of all nodes in j’s old fragment; if j has not sent a Report message yet, nodes in i’s old fragment starts finding its min. wt. outgoing edge, else not. • if j’s fragment level is less, no response sent and i just waits till j’s fragment id becomes higher • if fragment id’s match and j sends Connect to i also, merge into a level L+1 fragment with new core edge and id, and send initiate message
• some more details skipped, read paper • Algo. terminates when no outgoing edge found for a fragment • Worst case message complexity = O(n log n + m)
Fault Tolerance and Recovery
Fault Tolerance & Recovery Classification of faults: – based on component that failed • program/process • processor/machine • link • storage • clock – based on behavior of faulty component • Crash – just halts • Failstop – crash with additional conditions • Omission – fails to perform some steps • Byzantine – behaves arbitrarily • Timing – violates timing constraints
Types of tolerance: – Masking – system always behaves as per specifications even in presence of faults – Non-masking – system may violate specifications in presence of faults. Should at least behave in a well-defined manner Fault tolerant system should specify: – Class of faults tolerated – what tolerance is given from each class
Some building blocks (assumptions/primitives that help in designing fault tolerant systems): – Agreement (multiple processes agree on some value) – Clock synchronization – Stable storage (data accessible after crash) – Reliable communication (pointto-point, broadcast, multicast) – Atomic actions
Agreement Problems Model: – total n processes, at most m of which can be faulty – reliable communication medium – fully connected – receiver always knows the identity of the sender of a message – byzantine faults – synchronous system. In each round, a process receives messages, performs computation, and sends messages.
Different problem variations • Byzantine agreement (or Byzantine Generals problem) – one process x broadcasts a value v • all nonfaulty processes must agree on a common value (Agreement condition). • The agreed upon value must be v if x is nonfaulty (Validity condition) • Consensus – Each process broadcasts its initial value • satisfy agreement condition • If initial value of all nonfaulty processes is v, then the agreed upon value must be v
• Interactive Consistency – Each process i broadcasts its own value vi • all nonfaulty processes agree on a common vector (v1, v2, …,vn) • If the ith process is nonfaulty, then the ith value in the vector agreed upon by nonfaulty processes must be vi Solution to Byzantine agreement problem implies solution to other two
Byzantine Agreement Problem • no solution possible if – asynchronous system, or – n < (3m + 1) • needs at least (m+1) rounds of message exchange (lower bound result) • “Oral” messages – messages can be forged/changed in any manner, but the receiver always knows the sender
Lamport-Shostak-Pease Algorithm Recursively defined; OM(m), m > 0 • Source x broadcasts value to all processes • Let vi = value received by process i from source (0 if no value received). Process i acts as a new source and initiates OM(m -1), sending vi to remaining (n - 2) processes • For each i, j, i ≠ j, let v j = value received by process i from process j in step 2 using O(m-1). Process i uses the value majority(v1, v2, …, vn -1)
OM(0) 2. Source x broadcasts value to all processes 3. Each process uses the value; if no value received, 0 is used Time complexity = m+1 rounds Message Complexity = O(nm) You can reduce message complexity to polynomial by increasing time
Atomic Actions and Commit Protocols An action may have multiple subactions executed by different processes at different nodes of a distributed system Atomic action : either all subactions are done or none are done (all-ornothing property/ global atomicity property) as far as system state is concerned Commit protocols – protocols for enforcing global atomicity property
Two-Phase Commit • Assumes the presence of writeahead log at each process to recover from local crashes • One process acts as coordinator Phase 1: • coordinator sends COMMIT_REQUEST to all processes • waits for replies from all processes • on receiving a COMMIT_REQUEST, a process, if the local transaction is successful, writes Undo/redo logs in stable storage, and sends an AGREED message to the coordinator. Otherwise, sends an ABORT
Phase 2: • If all processes reply AGREED, coordinator writes COMMIT record into the log, then sends COMMIT to all processes. If at least one process has replied ABORT, coordinator sends ABORT to all. Coordinator then waits for ACK from all processes. If ACK is not received within timeout period, resend. If all ACKs are received, coordinator writes COMPLETE to log • On receiving a COMMIT, a process releases all resources/locks, and sends an ACK to coordinator • On receiving an ABORT, a process undoes the transaction using Undo log, releases all resources/locks, and sends an ACK
• Ensures global atomicity; either all processes commit or all of them aborts • Resilient to crash failures (see text for different scenarios of failure) • Blocking protocol – crash of coordinator can block all processes • Non-blocking protocols possible; ex., Three-Phase Commit protocol; we will not discuss in this class
Checkpointing & Rollback Recovery Error recovery: • Forward error recovery – assess damage due to faults exactly and repair the erroneous part of the system state – less overhead but hard to assess effect of faults exactly in general • Backward error recovery – on a fault, restore system state to a previous error-free state and restart from there – costlier, but more general, application-independent technique
Checkpoint and Rollback Recovery – a form of backward error recovery Checkpoint : – local checkpoint – local state of a process saved in stable storage for possible rollback on a fault – global checkpoint – collection of local checkpoints, one from each process Consistent and Strongly Consistent Global Checkpoint – similar to consistent and strongly consistent global state respectively (Also called “recovery line”)
Orphan message – a message whose receive is recorded in some local checkpoint of a global checkpoint but send is not recorded in any local checkpoint in that global checkpoint ( Note : A consistent global checkpoint cannot have an orphan message) Lost message – a message whose send is recorded but receive is not in a global checkpoint Is lost messages a problem?? – not if unreliable channels assumed (since messages can be lost anyway) – if reliable channels assumed, need to handle this properly! Cannot lose messages ! – We will assume unreliable channels for simplicity
Performance measures for a checkpointing and recovery algorithm • during fault-free operation – checkpointing time – space for storing checkpoints and messages (if needed) • in case of a fault – recovery time (time to establish recovery line) – extent of rollback (how far in the past did we roll back? how much computation is lost?) – is output commit problem handled? (if an output was sent out before the fault, say cash dispensed at a teller m/c, it should not be resent after restarting after the fault)
Some parameters that affect performance • Checkpoint interval (time between two successive checkpoints) • Number of processes • Communication pattern of the application • Fault frequency • Nature of stable storage
Classification of Checkpoint & Recovery Algorithms • Asynchronous/Uncoordinated – every process takes local checkpoint independently – to recover from a fault in one process, all processes coordinate to find a consistent global checkpoint from their local checkpoints – very low fault-free overhead, recovery overhead is high – Domino effect possible (no consistent global checkpoint exist, so all processes have to restart from scratch) – higher space requirements, as all local checkpoints need to be kept – Good for systems where fault is rare and inter-process communication is not too high (less chance of domino effect)
• Synchronous/Coordinated – all processes coordinate to take a consistent global checkpoint – during recovery, every process just rolls back to its last local checkpoint independently – low recovery overhead, but high checkpointing overhead – no domino effect possible – low space requirement, since only last checkpoint needs to be stored at each process
• Communication Induced – Synchronize checkpointing with communication, since message send/receive is the fundamental cause of inconsistency in global checkpoint – Ex. : take local checkpoint right after every send! Last local checkpoint at each process is always consistent. But too costly – Many variations are there, more efficient than the above, we will not discuss them in this class.
• Message logging – Take coordinated or uncoordinated checkpoint, and then log (in stable storage) all messages received since the last checkpoint – On recovery, only the recovering process goes back to its last checkpoint, and then replays messages from the log appropriately until it reaches the state right before the fault – Only class that can handle output commit problem! – Details too complex to discuss in this class
Some Checkpointing Algorithms Asynchronous/Uncoordinated – See Juang-Venkatesan’s algorithm in text, quite wellexplained Synchronous/Coordinated – Chandy-Lamport’s global state collection algorithm can be modified to handle recovery from faults – See Koo-Toueg’s algorithm in text, quite well-explained
