Abstract-Network Function Virtualization (NFV) enables mobile operators to virtualize their network entities as Virtualized Network Functions (VNFs), offering fine-grained on-demand network capabilities. VNFs can be dynamically scale-in/out to meet the performance desire and other dynamic behaviors. However, designing the auto-scaling algorithm for desired characteristics with low operation cost and low latency, while considering the existing capacity of legacy network equipment, is not a trivial task. In this paper, we propose a VNF Dynamic Auto Scaling Algorithm (DASA) considering the tradeoff between performance and operation cost. We develop an analytical model to quantify the tradeoff and validate the analysis through extensive simulations. The results show that the DASA can significantly reduce operation cost given the latency upper-bound. Moreover, the models provide a quick way to evaluate the cost-performance tradeoff and system design without wide deployment, which can save cost and time.
In this paper, we study birth/immigration-death processes under mild (binomial) catastrophes. We obtain explicit expressions for both the time-dependent (transient) and the limiting (equilibrium) factorial moments, which are then used to construct the transient and equilibrium distribution of the population size. We demonstrate that our approach is also applicable to multidimensional systems such as stochastic processes operating under a random environment and other variations of the model at hand. We also obtain various stochastic order results for the number of individuals with respect to the system parameters, as well as the relaxation time.
We consider basic M/M/c/c (c ≥ 1) retrial queues where the number of busy servers and that of customers in the orbit form a level-dependent quasi-birth-and-death (QBD) process with a special structure. Based on this structure and a matrix continued fraction approach, we develop an efficient algorithm to compute the joint stationary distribution of the numbers of busy servers and retrial customers. Through numerical experiments, we demonstrate that our algorithm works well even for M/M/c/c retrial queues with large value of c.
IntroductionThis paper considers M/M/c/c retrial queues, in which if an arriving customer finds an idle server, he starts to be served, otherwise he moves to a virtual orbit, stays there for an exponentially distributed time and retries to get service. Retrial queues arise in various systems such as telecommunications, computer networks and call centers [1,6,7,21,22,27,31]. Aguir et al. [1] investigate the impact of retrials on the performance of call centers, using a fluid approximation. Artalejo and Pla [6] further evaluate the effect of customer retrials on operations of telecommunication systems, by a retrial queue with
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