1 國立台灣大學 資訊工程學系 Chapter 6: Process Synchronization
2 資工系網媒所 NEWS 實驗室 Objectives To introduce the critical-section problem, whose solutions can be used to ensure the consistency of shared data To present both software and hardware solutions of the critical-section problem To introduce the concept of an atomic transaction and describe mechanisms to ensure atomicity /761
3 資工系網媒所 NEWS 實驗室 Module 6: Process Synchronization Background The Critical-Section Problem Peterson’s Solution Synchronization Hardware Semaphores Classic Problems of Synchronization Monitors Synchronization Examples Atomic Transactions /762
4 資工系網媒所 NEWS 實驗室 Background Concurrent access to shared data may result in data inconsistency Maintaining data consistency requires mechanisms to ensure the orderly execution of cooperating processes Suppose that we wanted to provide a solution to the consumer- producer problem that fills all the buffers. We can do so by having an integer count that keeps track of the number of full buffers. Initially, count is set to 0. It is incremented by the producer after it produces a new buffer and is decremented by the consumer after it consumes a buffer. /763
5 資工系網媒所 NEWS 實驗室 Producer while (true) { /* produce an item and put in nextProduced */ while (count == BUFFER_SIZE) ; // do nothing buffer [in] = nextProduced; in = (in + 1) % BUFFER_SIZE; count++; } Consumer while (true) { while (count == 0) ; // do nothing nextConsumed = buffer[out]; out = (out + 1) % BUFFER_SIZE; count--; /* consume the item in nextConsumed */ } /764
6 資工系網媒所 NEWS 實驗室 Race Condition count++ could be implemented as register1 = count register1 = register1 + 1 count = register1 count-- could be implemented as register2 = count register2 = register2 - 1 count = register2 Consider this execution interleaving with “count = 5” initially: S0: producer execute register1 = count {register1 = 5} S1: producer execute register1 = register1 + 1 {register1 = 6} S2: consumer execute register2 = count {register2 = 5} S3: consumer execute register2 = register2 - 1 {register2 = 4} S4: producer execute count = register1 {count = 6 } S5: consumer execute count = register2 {count = 4} /765
7 資工系網媒所 NEWS 實驗室 Solution to Critical-Section Problem 1.Mutual Exclusion - If process P i is executing in its critical section, then no other processes can be executing in their critical sections 2.Progress - If no process is executing in its critical section and there exist some processes that wish to enter their critical section, then the selection of the processes that will enter the critical section next cannot be postponed indefinitely 3.Bounded Waiting - A bound must exist on the number of times that other processes are allowed to enter their critical sections after a process has made a request to enter its critical section and before that request is granted Assume that each process executes at a nonzero speed No assumption concerning relative speed of the N processes /766
8 資工系網媒所 NEWS 實驗室 Algorithm (1) for Process P i P j do { while (turn != i) ; critical section turn = j; remainder section } while (1); do { while (turn != j) ; critical section turn = i; remainder section } while (1); /767
9 資工系網媒所 NEWS 實驗室 Algorithm (2) for Process P i P j do { flag[i] = TRUE; while (flag[j]) ; critical section flag[i] = false; remainder section } while (1); do { flag[j] = TRUE; while (flag[i]) ; critical section flag[j] = false; remainder section } while (1); /768
10 資工系網媒所 NEWS 實驗室 Peterson ’ s Solution Two-process solution Assume that the LOAD and STORE instructions are atomic; that is, cannot be interrupted. The two processes share two variables: int turn; Boolean flag[2] The variable turn indicates whose turn it is to enter the critical section. The flag array is used to indicate if a process is ready to enter the critical section. flag[i] = true implies that process P i is ready! /769
11 資工系網媒所 NEWS 實驗室 Algorithm (3) for Process P i P j while (true) { flag[i] = TRUE; turn = j; while ( flag[j] && turn == j); CRITICAL SECTION flag[i] = FALSE; REMAINDER SECTION } while (true) { flag[j] = TRUE; turn = i; while ( flag[i] && turn == i); CRITICAL SECTION flag[j] = FALSE; REMAINDER SECTION } /7610
12 資工系網媒所 NEWS 實驗室 Synchronization Hardware Many systems provide hardware support for critical section code Uniprocessors – could disable interrupts Currently running code would execute without preemption Generally too inefficient on multiprocessor systems Operating systems using this not broadly scalable Modern machines provide special atomic hardware instructions Atomic = non-interruptable Either test memory word and set value Or swap contents of two memory words /7611
13 資工系網媒所 NEWS 實驗室 Solution to Critical-section Problem Using Locks do { acquire lock critical section release lock remainder section } while (TRUE); /7612
14 資工系網媒所 NEWS 實驗室 TestAndndSet Instruction Definition: boolean TestAndSet (boolean *target) { boolean rv = *target; *target = TRUE; return rv: } /7613
15 資工系網媒所 NEWS 實驗室 Solution using TestAndSet Shared boolean variable lock., initialized to false. Solution: while (true) { while ( TestAndSet (&lock )) ; /* do nothing // critical section lock = FALSE; // remainder section } /7614
16 資工系網媒所 NEWS 實驗室 Swap Instruction Definition: void Swap (boolean *a, boolean *b) { boolean temp = *a; *a = *b; *b = temp: } /7615
17 資工系網媒所 NEWS 實驗室 Solution using Swap Shared Boolean variable lock initialized to FALSE; Each process has a local Boolean variable key. Solution: while (true) { key = TRUE; while ( key == TRUE) Swap (&lock, &key ); // critical section lock = FALSE; // remainder section } /7616
18 資工系網媒所 NEWS 實驗室 Bounded-waiting Mutual Exclusion with TestandSet() do { waiting[i] = TRUE; key = TRUE; while (waiting[i] && key) key = TestAndSet(&lock); waiting[i] = FALSE; // critical section j = (i + 1) % n; while ((j != i) && !waiting[j]) j = (j + 1) % n; if (j == i) lock = FALSE; else waiting[j] = FALSE; // remainder section } while (TRUE); /7617
19 資工系網媒所 NEWS 實驗室 Semaphore Synchronization tool that does not require busy waiting Semaphore S – integer variable Two standard operations modify S: wait() and signal() Originally called P() and V() Less complicated Can only be accessed via two indivisible (atomic) operations wait (S) { while S
20 資工系網媒所 NEWS 實驗室 Semaphore as General Synchronization Tool Counting semaphore – integer value can range over an unrestricted domain Binary semaphore – integer value can range only between 0 and 1; can be simpler to implement Also known as mutex locks Can implement a counting semaphore S as a binary semaphore Provides mutual exclusion Semaphore mutex; // initialized to 1 do { wait (mutex); // critical Section signal (mutex); // remainder section } while (TRUE); /7619
21 資工系網媒所 NEWS 實驗室 Semaphore Implementation Must guarantee that no two processes can execute wait () and signal () on the same semaphore at the same time Thus, implementation becomes the critical section problem where the wait and signal code are placed in the critical section. Could now have busy waiting in critical section implementation But implementation code is short Little busy waiting if critical section rarely occupied Note that applications may spend lots of time in critical sections and therefore this is not a good solution. /7620
22 資工系網媒所 NEWS 實驗室 With each semaphore there is an associated waiting queue. Each entry in a waiting queue has two data items: value (of type integer) pointer to next record in the list Two operations: block – place the process invoking the operation on the appropriate waiting queue. wakeup – remove one of processes in the waiting queue and place it in the ready queue. Semaphore Implementation with no Busy waiting (1/2) /7621
23 資工系網媒所 NEWS 實驗室 Semaphore Implementation with no Busy waiting (2/2) Implementation of wait: wait(semaphore *S) { S->value--; if (S->value < 0) { add this process to S->list; block(); } } Implementation of signal: signal(semaphore *S) { S->value++; if (S->value list; wakeup(P); } } /7622
24 資工系網媒所 NEWS 實驗室 Deadlock and Starvation Deadlock – two or more processes are waiting indefinitely for an event that can be caused by only one of the waiting processes Let S and Q be two semaphores initialized to 1 P0P1P0P1 wait (S); wait (Q); wait (Q); wait (S);...… signal (S); signal (Q); signal (Q); signal (S); Starvation – indefinite blocking. A process may never be removed from the semaphore queue in which it is suspended. Priority Inversion - Scheduling problem when lower-priority process holds a lock needed by higher-priority process /7623
25 資工系網媒所 NEWS 實驗室 Priority Inversion /7624
26 資工系網媒所 NEWS 實驗室 Priority Inheritance /7625
27 資工系網媒所 NEWS 實驗室 Classical Problems of Synchronization Bounded-Buffer Problem Readers and Writers Problem Dining-Philosophers Problem /7626
28 資工系網媒所 NEWS 實驗室 Bounded-Buffer Problem (1/2) N buffers, each can hold one item Semaphore mutex initialized to the value 1 Semaphore full initialized to the value 0 Semaphore empty initialized to the value N. /7627
29 資工系網媒所 NEWS 實驗室 Bounded Buffer Problem (2/2) producer process do { // produce an item wait (empty); wait (mutex); // add the item to the buffer signal (mutex); signal (full); } while (TRUE); consumer process do { wait (full); wait (mutex); // remove an item from buffer signal (mutex); signal (empty); // consume the item } while (TRUE); /7628
30 資工系網媒所 NEWS 實驗室 Readers-Writers Problem (1/3) A data set is shared among a number of concurrent processes Readers – only read the data set; they do not perform any updates Writers – can both read and write Problem – allow multiple readers to read at the same time. Only one single writer can access the shared data at the same time Shared Data Data set Semaphore mutex initialized to 1 Semaphore wrt initialized to 1 Integer readcount initialized to 0 /7629
31 資工系網媒所 NEWS 實驗室 Readers-Writers Problem (2/3) The structure of a writer process do { wait (wrt) ; // writing is performed signal (wrt) ; } while (TRUE); /7630
32 資工系網媒所 NEWS 實驗室 Readers-Writers Problem (3/3) The structure of a reader process do { wait (mutex) ; readcount ++ ; if (readcount == 1) wait (wrt) ; signal (mutex) // reading is performed wait (mutex) ; readcount - - ; if (readcount == 0) signal (wrt) ; signal (mutex) ; } while (TRUE); /7631
33 資工系網媒所 NEWS 實驗室 Dining-Philosophers Problem (1/2) Shared data Bowl of rice (data set) Semaphore chopstick [5] initialized to 1 /7632
34 資工系網媒所 NEWS 實驗室 Dining-Philosophers Problem (2/2) The structure of Philosopher i: While (true) { wait ( chopstick[i] ); wait ( chopStick[ (i + 1) % 5] ); // eat signal ( chopstick[i] ); signal (chopstick[ (i + 1) % 5] ); // think } /7633
35 資工系網媒所 NEWS 實驗室 Problems with Semaphores Correct use of semaphore operations: signal (mutex) …. wait (mutex) wait (mutex) … wait (mutex) Omitting of wait (mutex) or signal (mutex) (or both) /7634
36 資工系網媒所 NEWS 實驗室 二元號誌 (1/2) - binary semaphore 二元號誌的值只限定為 0 或 1 。 利用硬體對二元數值的運算支援,二元號誌 的實作要比計數號誌簡單快速得多。 可以利用二元號誌來實作計數號誌。 /7635
37 資工系網媒所 NEWS 實驗室 二元號誌 (2/2) 計數號誌可以利用兩個二元號誌以及一個 整數實作。 void wait(S) { wait(S1); C--; if (C < 0) { signal(S1); wait(S2); } signal(S1); } void signal(S) { wait( S1); C++; if (C
38 資工系網媒所 NEWS 實驗室 臨界區域 (1/4) - critical region 臨界區域的使用非常方便。 以下宣告一個具有共享變數 v 的臨界區域, 在 B 條件式成立下,如果沒有其他行程在此 臨界區域中執行,就會執行 S 敘述: 利用臨界區域來實作,程式設計師不用煩 惱同步的問題,只要正確地把問題描述在 臨界區域內。 有限緩衝區問題可以用臨界區域來簡單地 解決同步的問題。 region v when B do S; /7637
39 資工系網媒所 NEWS 實驗室 臨界區域 (2/4) 生產者與消耗者程式可以分別以臨界區域 實作如下。 region buffer when (count < n) { pool[in] = nextp; in = (in + 1) % n; count++; } region buffer when (count > 0) { nextc = pool[out]; out = (out + 1) % n; count--; } 生 產 者生 產 者消 耗 者消 耗 者 /7638
40 資工系網媒所 NEWS 實驗室 臨界區域 (3/4) 臨界區域 region v when B do S 可利用 mutex 、 first_delay 及 second_delay 三個號誌實作。 mutex 號誌是用來確保臨界區的互斥條件成立。 如果行程因為 B 為 FALSE 而無法進入臨界區,該行 程將會在號誌 first_delay 等待。 在號誌 first_delay 等待的行程重新檢查 B 值之前,會 離開號誌 first_delay ,而在號誌 second_delay 等待。 分成 first_delay 與 second_delay 兩段式等待的原因,是 為了要避免行程持續忙碌地檢查 B 值。 當一個行程離開了臨界區之後,可能因為執行了敘述 S 而改變了 B 的值,所以需要重新檢查。 /7639
41 資工系網媒所 NEWS 實驗室 臨界區域 (4/4) wait(mutex); while (!B) { first_count++; if (second_count > 0) signal(second_delay); else signal(mutex); wait(first_delay); first_count--; second_count++; if (first_count > 0) signal(first_delay); else signal(second_delay); wait(second_delay); second_count--; } S; if (first_count > 0) signal(first_delay); else if (second_count > 0) signal(second_delay); else signal(mutex); wait(mutex); while (!B) { first_count++; if (first_count > 0) signal(first_delay); else signal(mutex); wait(first_delay); first_count--; first_count++; if (first_count > 0) signal(first_delay); else signal(first_delay); wait(first_delay); first_count--; } S; if (first_count > 0) signal(first_delay); else if (first_count > 0) signal(first_delay); else signal(mutex); wait(mutex); while (!B) { first_count++; if (first_count > 0) signal(first_delay); else signal(mutex); wait(first_delay); first_count--; } S; if (first_count > 0) signal(first_delay); else signal(mutex); wait(mutex); while (!B) { first_count++; signal(mutex); wait(first_delay); first_count--; } S; if (first_count > 0) signal(first_delay); else signal(mutex); /7640
42 資工系網媒所 NEWS 實驗室 Monitors A high-level abstraction that provides a convenient and effective mechanism for process synchronization Only one process may be active within the monitor at a time monitor monitor-name { // shared variable declarations procedure P1 (…) { …. } … procedure Pn (…) {……} Initialization code ( ….) { … } … } } /7641
43 資工系網媒所 NEWS 實驗室 Schematic view of a Monitor /7642
44 資工系網媒所 NEWS 實驗室 Condition Variables condition x, y; Two operations on a condition variable: x.wait () – a process that invokes the operation is suspended. x.signal () – resumes one of processes (if any) that invoked x.wait () /7643
45 資工系網媒所 NEWS 實驗室 Solution to Dining Philosophers (1/3) monitor DP { enum { THINKING; HUNGRY, EATING) state [5] ; condition self [5]; void pickup (int i) { state[i] = HUNGRY; test(i); if (state[i] != EATING) self [i].wait; } void putdown (int i) { state[i] = THINKING; // test left and right neighbors test((i + 4) % 5); test((i + 1) % 5); } /7644
46 資工系網媒所 NEWS 實驗室 Solution to Dining Philosophers (2/3) void test (int i) { if ( (state[(i + 4) % 5] != EATING) && (state[i] == HUNGRY) && (state[(i + 1) % 5] != EATING) ) { state[i] = EATING ; self[i].signal () ; } initialization_code() { for (int i = 0; i < 5; i++) state[i] = THINKING; } /7645
47 資工系網媒所 NEWS 實驗室 Solution to Dining Philosophers (3/3) Each philosopher I invokes the operations pickup() and putdown() in the following sequence: dp.pickup (i) EAT dp.putdown (i) /7646
48 資工系網媒所 NEWS 實驗室 Monitor Implementation Using Semaphores Variables semaphore mutex; // (initially = 1) semaphore next; // (initially = 0) int next-count = 0; Each procedure F will be replaced by wait(mutex); … body of F; … if (next_count > 0) signal(next) else signal(mutex); Mutual exclusion within a monitor is ensured. /7647
49 資工系網媒所 NEWS 實驗室 Monitor Implementation For each condition variable x, we have: semaphore x_sem; // (initially = 0) int x-count = 0; The operation x.wait can be implemented as: x-count++; if (next_count > 0) signal(next); else signal(mutex); wait(x_sem); x-count--; /7648
50 資工系網媒所 NEWS 實驗室 Monitor Implementation The operation x.signal can be implemented as: if (x-count > 0) { next_count++; signal(x_sem); wait(next); next_count--; } /7649
51 資工系網媒所 NEWS 實驗室 semaphore mutex; // (initially = 1) semaphore next; // (initially = 0) int next-count = 0; semaphore x-sem; // (initially = 0) int x-count = 0; wait(mutex); … body of F; … if (next-count > 0) signal(next) else signal(mutex); if (x-count > 0) { next-count++; signal(x-sem); wait(next); next-count--; } x-count++; if (next-count > 0) signal(next); else signal(mutex); wait(x-sem); x-count--; x.wait() x.sign al() /7650
52 資工系網媒所 NEWS 實驗室 A Monitor to Allocate Single Resource monitor ResourceAllocator { boolean busy; condition x; void acquire(int time) { if (busy) x.wait(time); busy = TRUE; } void release() { busy = FALSE; x.signal(); } initialization code() { busy = FALSE; } /7651
53 資工系網媒所 NEWS 實驗室 Synchronization Examples Solaris Windows XP Linux Pthreads /7652
54 資工系網媒所 NEWS 實驗室 Solaris Synchronization Implements a variety of locks to support multitasking, multithreading (including real-time threads), and multiprocessing Uses adaptive mutexes for efficiency when protecting data from short code segments Uses condition variables and readers-writers locks when longer sections of code need access to data Uses turnstiles to order the list of threads waiting to acquire either an adaptive mutex or reader-writer lock /7653
55 資工系網媒所 NEWS 實驗室 Windows XP Synchronization Uses interrupt masks to protect access to global resources on uniprocessor systems Uses spinlocks on multiprocessor systems Also provides dispatcher objects which may act as either mutexes and semaphores Dispatcher objects may also provide events An event acts much like a condition variable /7654
56 資工系網媒所 NEWS 實驗室 Linux Synchronization Linux: Prior to kernel Version 2.6, disables interrupts to implement short critical sections Version 2.6 and later, fully preemptive Linux provides: semaphores spin locks Single processorMultiple Processor Disable Kernel preemption Acquire spin lock Enable Kernel preemption Release spin lock /7655
57 資工系網媒所 NEWS 實驗室 Pthreads Synchronization Pthreads API is OS-independent It provides: mutex locks condition variables Non-portable extensions include: read-write locks spin locks /7656
58 資工系網媒所 NEWS 實驗室 Atomic Transactions System Model Log-based Recovery Checkpoints Concurrent Atomic Transactions /7657
59 資工系網媒所 NEWS 實驗室 System Model Assures that operations happen as a single logical unit of work, in its entirety, or not at all Related to field of database systems Challenge is assuring atomicity despite computer system failures Transaction - collection of instructions or operations that performs single logical function Here we are concerned with changes to stable storage – disk Transaction is series of read and write operations Terminated by commit (transaction successful) or abort (transaction failed) operation Aborted transaction must be rolled back to undo any changes it performed /7658
60 資工系網媒所 NEWS 實驗室 Transactional Memory (TM) TM provides an alternative strategy for developing a thread-save concurrent applications. A memory transaction is a sequence of memory read- write operations that are atomic. As the number of threads increases, traditional locking does not scale well. STM – Software TM Inserting instrumentation code inside transaction blocks by a compiler HTM – Hardware TM Need to modify cache hierarchy and cache coherency protocol /7659
61 資工系網媒所 NEWS 實驗室 Types of Storage Media Volatile storage – information stored here does not survive system crashes Example: main memory, cache Nonvolatile storage – Information usually survives crashes Example: disk and tape Stable storage – Information never lost Not actually possible, so approximated via replication or RAID to devices with independent failure modes The goal is to assure transaction atomicity where failures cause loss of information on volatile storage /7660
62 資工系網媒所 NEWS 實驗室 Log-Based Recovery Record to stable storage information about all modifications by a transaction Most common is write-ahead logging Log on stable storage, each log record describes single transaction write operation, including Transaction name Data item name Old value New value written to log when transaction T i starts written when T i commits Log entry must reach stable storage before operation on data occurs /7661
63 資工系網媒所 NEWS 實驗室 Log-Based Recovery Algorithm Using the log, system can handle any volatile memory errors Undo(T i ) restores value of all data updated by T i Redo(T i ) sets values of all data in transaction T i to new values Undo(T i ) and redo(T i ) must be idempotent Multiple executions must have the same result as one execution If system fails, restore state of all updated data via log If log contains without, undo(T i ) If log contains and, redo(T i ) /7662
64 資工系網媒所 NEWS 實驗室 Checkpoints Log could become long, and recovery could take long Checkpoints shorten log and recovery time. Checkpoint scheme: 1. Output all log records currently in volatile storage to stable storage 2. Output all modified data from volatile to stable storage 3. Output a log record to the log on stable storage Now recovery only includes T i, such that T i started executing before the most recent checkpoint, and all transactions after T i All other transactions already on stable storage /7663
65 資工系網媒所 NEWS 實驗室 Concurrent Transactions Must be equivalent to serial execution – serializability Could perform all transactions in critical section Inefficient, too restrictive Concurrency-control algorithms provide serializability /7664
66 資工系網媒所 NEWS 實驗室 Serializability Consider two data items A and B Consider Transactions T 0 and T 1 Execute T 0, T 1 atomically Execution sequence called schedule Atomically executed transaction order called serial schedule For N transactions, there are N! valid serial schedules /7665
67 資工系網媒所 NEWS 實驗室 Serial Schedule 1: T 0 then T 1 /7666
68 資工系網媒所 NEWS 實驗室 Nonserial Schedule Nonserial schedule allows overlapped execute Resulting execution not necessarily incorrect Consider schedule S, consecutive operations O i, O j Conflict if access same data item, with at least one write If O i, O j consecutive and operations of different transactions & O i and O j don’t conflict Then S’ with swapped order O j O i equivalent to S If S can become a serial S’ via swapping nonconflicting operations S is conflict serializable /7667
69 資工系網媒所 NEWS 實驗室 Schedule 2: Concurrent Serializable Schedule /7668
70 資工系網媒所 NEWS 實驗室 Locking Protocol Ensure serializability by associating lock with each data item Follow locking protocol for access control Locks Shared – T i has shared-mode lock (S) on item Q, T i can read Q but not write Q Exclusive – T i has exclusive-mode lock (X) on Q, T i can read and write Q Require every transaction on item Q acquire appropriate lock If lock already held, new request may have to wait Similar to readers-writers algorithm /7669
71 資工系網媒所 NEWS 實驗室 Two-phase Locking Protocol Generally ensures conflict serializability Each transaction issues lock and unlock requests in two phases Growing – obtaining locks Shrinking – releasing locks Does not prevent deadlock /7670
72 資工系網媒所 NEWS 實驗室 Timestamp-based Protocols Select order among transactions in advance – timestamp-ordering Transaction T i associated with timestamp TS(T i ) before T i starts TS(T i ) < TS(T j ) if Ti entered system before T j TS can be generated from system clock or as logical counter incremented at each entry of transaction Timestamps determine serializability order If TS(T i ) < TS(T j ), system must ensure produced schedule equivalent to serial schedule where T i appears before T j /7671
73 資工系網媒所 NEWS 實驗室 Timestamp-based Protocol Implementation Data item Q gets two timestamps W-timestamp(Q) – largest timestamp of any transaction that executed write(Q) successfully R-timestamp(Q) – largest timestamp of successful read(Q) Updated whenever read(Q) or write(Q) executed Timestamp-ordering protocol assures any conflicting read and write executed in timestamp order Suppose T i executes read(Q) If TS(T i ) < W-timestamp(Q), T i needs to read value of Q that was already overwritten read operation rejected and T i rolled back If TS(T i ) ≥ W-timestamp(Q) read executed, R-timestamp(Q) set to max(R-timestamp(Q), TS(T i )) /7672
74 資工系網媒所 NEWS 實驗室 Timestamp-ordering Protocol Suppose Ti executes write(Q) If TS(T i ) < R-timestamp(Q), value Q produced by T i was needed previously and T i assumed it would never be produced Write operation rejected, T i rolled back If TS(T i ) < W-tiimestamp(Q), T i attempting to write obsolete value of Q Write operation rejected and T i rolled back Otherwise, write executed Any rolled back transaction T i is assigned new timestamp and restarted Algorithm ensures conflict serializability and freedom from deadlock /7673
75 資工系網媒所 NEWS 實驗室 Schedule Possible Under Timestamp Protocol /7674
76 國立台灣大學 資訊工程學系 End of Chapter 6