银行家算法（Banker's Algorithm）

•Multiple instances.

•Each process must a priori claim maximum use.

•When a process requests a resource it may have to wait.  

•When a process gets all its resources it must return them in a finite amount of time.

n为进程的数目，m为资源类型的数目

•Available:  Vector of length m.

–If available [j] = k, there are k instances of resource type Rj available.（如果available[j]=k,那么资源Rj有k个实例可用）

•Max: n x m matrix. 

–If Max [i,j] = k, then process Pi may request at most k instances of resource type Rj.（如果Max[i,j]=k,那么进程Pi可以最多请求资源Rj的k个实例）

Data Structures for the Banker’s Algorithm (Cont.):

•Allocation:  n x m matrix. 

–If Allocation[i,j] = k then Pi is currently allocated k instances of Rj.（如果Allocation[i,j]=k,那么进程Pi当前分配了k个资源Rj的实例）

•Need:  n x m matrix.

–If Need[i,j] = k, then Pi may need k more instances of Rj to complete its task.（如果Need[i,j]=k,那么进程Pi 还需要k个资源Rj的实例）

  Need [i,j] = Max[i,j] – Allocation [i,j].

Safety Algorithm（安全算法）:

1.  Let Work and Finish be vectors of length m and n, respectively.  Initialize（让Work和Finish作为长度为m和n的向量）

Work := Available

Finish [i] = false fori - 1,3, …, n.

2.  Find an isuch that both: （找到i）

(a) Finish [i] = false

(b) Needi£Work

If no such iexists, go to step 4.

3.  Work := Work + Allocationi
Finish[i] := true
go to step 2.

If Finish [i] = true for all i, then the system is in a safe state.

Resource-Request Algorithm for Process Pi

•Requesti = request vector for process Pi. 

1.  If Requesti £ Needi go to step 2.  Otherwise, raise error condition, since process has exceeded its maximum claim.

2.  If Requesti £ Available, go to step 3.  Otherwise Pi  must wait, since resources are not available.

3.  Pretend to allocate requested resources to Pi by modifying the state as follows:假定给Pi 分配资源

  Available := Available - Requesti;

  Allocationi := Allocationi + Requesti;

  Needi := Needi – Requesti

4.用安全算法进行检查,看系统是否处于安全状态

•If safe Þ the resources are allocated to Pi.

•If unsafe Þ Pi must wait, and the old resource-allocation state is restored

 

Example of Banker’s Algorithm:

•5 processes P0 through P4; 3 resource types A (10 instances),
B (5instances), and C (7 instances).（5个进程P0-P4,3类资源A(10个实例），B（5个实例），C（7个实例））

•Snapshot at time T0:（时刻T0的片段）

   Allocation       Max       Available

     A B C          A B C        A B C

P0  0 1 0          7 5 3         3 3 2

P1  2 0 0          3 2 2 

P2  3 0 2          9 0 2

P3  2 1 1          2 2 2

P4  0 0 2          4 3 3 

•The content of the matrix. Need is defined to be Max – Allocation. （ Need矩阵的内容可以由Max – Allocation 计算出来）

  Need

        A B C

   P0  7 4 3

   P1  1 2 2

   P2  6 0 0

   P3  0 1 1

   P4  4 3 1 

•用安全检测算法看能否找到一个安全序列

–Work[]=available=(3,3,2)

–Finish[i]=false  (i=0..4)

–      

–       Work    need   allocation   finish

– P1   3 3 2    1 2 2    2 0 0       T

– P3   5 3 2    0 1 1    2 1 1       T

– P4   7 4 3    4 3 1    0 0 2       T

– P2   7 4 5    6 0 0    3 0 2       T

– P0  10 4 7    7 4 3    0 1 0       T

–存在安全序列：（P1，P3，P4，P2，P0）

 

注意两点：

1、通常，安全序列不唯一；

2、安全序列中的选取，总是将work中的资源首先分给need（Pi）<=work且max{allocation(Pi)}的进程，剩下的依次类推分配