In this paper, we consider a general class of a queuing system with multiple job types and flexible service facility. We use a stochastic control policy to determine the performance loss in multi-class M/M/1 queue. The considered system is originally a Markov decision processes (MDP). The author showed how to compute performance bounds for the stochastic control policy of MDP with an average cost criteria. In practice, many authors used heuristic control policies due to some hardness in computing and running mathematically optimal policies. The authors found bounds on performance in order to an optimal policy where the goal of this job is to compute the difference of optimality and a specific policy. In other words, this study shows that, the optimal bounds of the average queue length for any non-idling policies can be found by a factor of service rates.
We consider resource allocation problem in the cloud computing. We use queuing model to model the process of entering into the cloud and to schedule and to serve incoming jobs. In this paper, the main problem is to allocate resources in the queuing systems as a general optimization problem for controlled Markov process with finite state space. For this purpose, we study a model of cloud computing where the arrival jobs follow a stochastic process. We reduce this problem to a routing problem. In the case of minimizing, cost is given as a mixture of an average queue length and number of lost jobs. We use dynamic programming approach. Finally, we obtain the explicit form of the optimal control by the Bellman equation.
Cloud computing is known as a new trend for computing resource provision. The process of entering into the cloud is formed as queue, so that each user has to wait until the current user is being served. In this model, the web applications are modeled as queues and the virtual machines are modeled as service centers. M/M/K model is used for multiple priority and multiple server systems with preemptive priorities. To achieve that it distinguish two groups of priority classes that each classes includes multiple items, each having their own arrival and service rate. It derives an approximate method to estimate the steady state probabilities. Based on these probabilities, it can derives approximations for a wide range of relevant performance characteristics, such as the expected postponement time for each item class and the first and second moment of the number of items of a certain type in the system.
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