Copyright 2011, A Resource Allocation Mechanism of Data Center for Public Cloud Service Copyright 2011, Outline Introduction Scenario and settings A branch and bound approach Discussion and ongoing works Copyright 2011, Introduction Dealing with Number of active servers, number of VMs for each application, VM placement problem, and optimization over a series of time slots. Apply an existing load-prediction method to get the forecast of resource demand of each application over a series of time slots. Copyright 2011, Scenario and Settings All servers and VMs have fixed capacity. When the workload of an application changes, we readjust the number of VMs dedicated to that application. Copyright 2011, Scenario and Settings The Power Consumption Model Copyright 2011, Scenario and Settings The Cost Function Thus, for the operating cost, we define P idle as the basic energy cost in a time slot when a server is idle, and as the incremental energy cost in a time slot every time when we add in a new VM. For the switching cost, we define s as the cost to switch on/off a server, and v as the cost to switch on/off a VM. Copyright 2011, Scenario and Settings The Cost Function The cost function will be the sum of operating cost and switching cost, considering all running servers and VMs. Suppose there are T time slots in our scenario, then the objective function will be the minimization of cost function over T time slots, subject to the number of hosted VMs must not exceed the server capacity. Copyright 2011, A Branch-and-Bound Approach Problem Simplification Claim 1: The solution of optimum(# of servers, # of VMs) is a superset of the solution of optimum(# of servers, #number of VMs, VM placement). Thus, we can apply a two-pass algorithm to reduce the complexity of the problem. Copyright 2011, A Branch-and-Bound Approach Problem Simplification Claim 2: When doing pass1 of the algorithm, we only need to consider the concave upwards parts. Copyright 2011, A Branch-and-Bound Approach Use the branch and bound approach to find the optimal solution of (# of servers, # of VMs). Given the status of source and sink, the resource demand of each time slot, find a minimal weighted path from source to sink. Copyright 2011, A Branch-and-Bound Approach Problem Complexity A simple relation to decide when to keep the unnecessary VM is < 2v, and for the server, it is P idle < 2s, is the time interval by that we need the resource again. The problem comes when that VM is the last remaining VM on that server, or, last two VMs from two apps, and so on. What is more, the result of deciding # of VMs will affect the way deciding # of servers. Its hard to find a simple way to find the optimal solution. Copyright 2011, A Branch-and-Bound Approach Main Idea The key idea of the BB algorithm is: if the lower bound for some tree node A is greater than the upper bound for some other node B, then A may be safely discarded from the search. A global upper bound: the minimum cost among all accomplished paths so far. The lower bound of each node: current accumulated cost + minimum remaining operating cost + switching cost to the status of sink node Copyright 2011, A Branch-and-Bound Approach A Paradigm Set = 1.0, P idle = 0.5, v = 0.6, s = 0.7 Copyright 2011, A Branch-and-Bound Approach Tree Structure Suppose there are n applications, define the resource provision tuple as a (n+1)-tuple. The 1 st element represents the # of active servers, the 2 nd element represents the # of VMs for the first app, and i-th element represents the # of VMs for the (i-1)-th app. A search tree with depth T. Every node consists of a resource provision tuple, the current accumulated cost field and lower bound field. Using doubly linked list. A path can be represented by its tail node and backtracked to its preceding nodes. Copyright 2011, A Branch-and-Bound Approach Branch Table When it happens a resource demand degradation, it may be worthy of keeping the VM if < 2v. The false-positive is allowed. Construct a branch table composed of T resource provision tuple. Each element in the tuple indicates how many possible branches of # of VMs for that app. Copyright 2011, A Branch-and-Bound Approach Branch Table Similarly, for the server field in the tuple, consider P idle < 2s. Note that the total server capacity must accommodate the maximal possible number of VMs in that time slot. From a certain node, the possible number of branches in the next time slot is the product of all elements of that tuple. Copyright 2011, A Branch-and-Bound Approach Shortcut Table A shortcut is a discovered path from a certain time slot to the sink node with minimal cost. In the shortcut table, every time slot records a discovered best path and its cost. Note that the shortcut of (t = a) is not necessarily contained in shortcut of (t = b), for any a < b. Copyright 2011, A Branch-and-Bound Approach Shortcut Table Updating shortcut table: every time when we finish a path to the sink node. The cost of a shortcut is reversely accumulated. Applying shortcut: apply a shortcut when (current accumulated cost + shortcut cost + switching cost transferring to shortcut) < upper bound. The reason of using shortcut : To reduce the complexity of the algorithm, we must discard nodes as early as possible. It is possible to lower the upper bound only when we finish another path to the sink. Copyright 2011, A Branch-and-Bound Approach The Whole Procedure The baseline path: the minimal operating path. Using a priority depth-first search. Copyright 2011, Discussion and Ongoing Works The worst case complexity is still extremely high. We dont know the effectiveness of the those acceleration method. Need to prove or analyze those two claims. Need an approach to deal with the VM placement problem.