Support more backoff functions

Introduce more backoff functions to Zaqar.

Change-Id: I5bf310f31d632cbd06447e0675084f1ac86fe30a

specs/queens/index.rst

@@ -7,3 +7,4 @@
    :maxdepth: 2
 
    support-redis-as-mgmt-storage-backend
+   support-more-backoff-functions

specs/queens/support-more-backoff-functions.rst

@@ -0,0 +1,194 @@
+..
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+
+===============================
+Support More Backoff Functions
+===============================
+
+https://blueprints.launchpad.net/zaqar/+spec/support-more-backoff-functions
+
+Sometimes, because of network/internet connection issue or the load of the
+target services/applications, the notification sent from Zaqar to the
+subscriber may fail. That means there is no retries if endpoint has some
+problem that can't receive the notification. For users or applications,
+it's missing important message without notification. To solve this problem,
+Zaqar has supported notification delivery policy in pike release [1].
+
+Problem description
+====================
+
+Now that Zaqar has supported only linear retry backoff function in Pike
+release,it increases the delay time linearly from minimum delay to maximum
+delay. We will support more retry backoff functions in Zaqar now.
+
+Fortunately, AWS SNS service has supported the policy, that would be a good
+reference for Zaqar[2].
+
+Proposed change
+================
+
+For clarification what we want to do, there are some questions to be answered:
+
+1. How many retry backoff functions Will Zaqar support?
+
+You can choose from four retry backoff functions as follows:
+
+* Linear.
+* Arithmetic.
+* Geometric.
+* Exponential.
+
+
+2. What difference between these four retry backoff functions?
+
+ As we can see the picture in chapter Backoff Phase in [2], The screen shot
+ shows how each retry backoff function affects the delay associated with
+ messages during the backoff period. The vertical axis represents the delay
+ in seconds associated with each of the 10 retries. The horizontal axis
+ represents the retry number. The  minimum delay is 5 seconds, and the
+ maximum delay is 260 seconds.
+
+
+3. The formula of these four retry backoff functions
+
+  Generally, we assume that the minimum delay is MIN, the maximum delay is
+  MAX, and the total retry number is NUM. From three element above, we can
+  conclude the formula of these four retry backoff functions.
+
+* Linear.
+
+  LINEAR_INTERVAL = ( MAX - MIN ) / NUM
+  time1 = MIN
+  time2 = MIN + LINEAR_INTERVAL*1
+  time3 = MIN + LINEAR_INTERVAL*2
+  timen = MIN + LINEAR_INTERVAL*(n-1)
+  timeN = MAX
+
+  The Linear retry backoff functions has already been implemented in Pike
+  release, we only list here for reference and comparing.
+
+* Geometric
+
+  we assume the common ratio of a geometric series is K:
+  time1 = MIN
+  time2 = K * MIN
+  time3 = K^2 * MIN
+  timen = K^(n-1) * MIN
+  timeN = K^(NUM-1) * MIN = MAX
+
+  so :
+
+  K^(NUM-1) = MAX/MIN
+  lg[ K^(NUM-1) ] = lg( MAX/MIN )
+  (NUM-1) * lg(K) = lg( MAX/MIN )
+  lg(K) = lg( MAX/MIN ) / (NUM-1)
+  K = 10^[  lg( MAX/MIN ) / (NUM-1) ]
+
+  Finally:
+
+  timen = {10^[  lg( MAX/MIN ) / (NUM-1) ]}^(n-1) * MIN
+
+* Exponential.
+
+  we assume the  power exponent of a exponential series is k, coefficient is p:
+
+  the general function of power exponent of a exponential series is:
+  y = p * k^x
+
+  time1 = MIN = p*k^1
+  timeN = MAX = p*k^NUM
+  MAX/MIN = k^(NUM-1)
+  lg(MAX/MIN) = (NUM-1)*lg(k)
+  lg(k) = lg(MAX/MIN)/ (NUM-1)
+  k = 10^[lg(MAX/MIN)/ (NUM-1)]
+  p = MIN/{10^[lg(MAX/MIN)/ (NUM-1)]}
+
+  Finally:
+
+  timen = p*k^n
+  timen = MIN/{10^[lg(MAX/MIN)/ (NUM-1)]} * {10^[lg(MAX/MIN)/ (NUM-1)]} ^n
+
+* Arithmetic.
+
+  we assume the common difference of a arithmetic series is d:
+
+  time1 = MIN
+  time2 = time1 + d*1
+  time3 = time2 + d*2
+  time4 = time3 + d*3
+
+  timen = timen-1 + d*(n-1)
+
+  timeN = timeN-1 + d*(NUM-1) = MAX
+
+  So:
+  timeN - time1 = NUM*(NUM-1)/2*d
+
+  d = 2*(MAX-MIN)/[NUM*(NUM-1)]
+
+  timen - time1 = n*(n-1)/2 * { 2*(MAX-MIN)/[NUM*(NUM-1)] }
+
+  Finally:
+
+  timen  = n*(n-1)/2 * { 2*(MAX-MIN)/[NUM*(NUM-1)] } + MIN
+
+4. What changes will bring into Zaqar?
+
+* First, we will define three functions according to formula of these retry
+  backoff functions.
+
+* Second, change the logic of notification, when fail is existing when sending
+  notification to endpoint, then use the policy which has binded to this
+  subscription to make retries. In Backoff Phase, we will select the retry
+  backoff functions according to user choice to resend notification.
+
+
+Drawbacks
+---------
+
+N/A
+
+Alternatives
+------------
+
+N/A
+
+Implementation
+==============
+
+Assignee(s)
+-----------
+
+Primary assignee:
+  gecong (ge.cong@zte.com.cn)
+
+Milestones
+----------
+
+Q-2
+
+Work Items
+----------
+
+* Add three functions according to formula of these retry
+  backoff functions.
+* Change the Backoff Phase of notification process for applying the retry
+  backoff functions.
+* UTs for this feature.
+
+
+Dependencies
+=============
+
+
+[1]:https://specs.openstack.org/openstack/zaqar-specs/specs/pike/notification-delivery-policy.html
+[2]:http://docs.aws.amazon.com/sns/latest/dg/DeliveryPolicies.html