Performance Implications of Fluctuating Server Capacity Jingxiang Luo Carey Williamson Department of Computer Science University of Calgary {jxluo,carey}@cpsc.ucalgary.ca Abstract In this paper, we consider a variant of an M/M/c/c loss sys- tem with fluctuating server capacity. Given a set of primary inputs, such as arrival rate, service rate, and capacity fluctua- tion rate, we develop a detailed model using MRGP, such that blocking and dropping metrics can be calculated explicitly. To gain insight into performance implications of a stochastic capacity queue, we conduct an analysis on a simple, approx- imate model. We investigate the functional behaviour of the system, using both the approximate and the detailed model. The significance of results in the context of network perfor- mance evaluation and capacity planning is highlighted. Keywords: network capacity planning, stochastic capacity, loss system, MRGP 1. INTRODUCTION Server capacity is the primary determinant of system per- formance. Network provisioning involves determining a suit- able configuration of system capacity (service dimensioning) in order to achieve desired performance targets for metrics such as blocking or delay. In most systems, the server capacity is a constant value. An illustrative example is used in telephony: the Erlang B formula expresses the call blocking probability in terms of traffic intensity and the trunk capacity. The number of lines required for a target blocking probability can be decided by using such a formula. For the design and QoS provisioning of next-generation networks, capacity planning is an important issue. However, there is no corresponding formula as robust as the Erlang for- mula. This is mainly due to the complicated nature of com- puter networks: heterogeneous traffic, service differentiation policies, and the noisy environment for wireless networks. Server capacity is the number of parallel service channels plus the number of buffers. Consider a server with capacity C, where C is a random variable. This system experiences two types of losses: blocking when an arrival encounters a full system, and dropping when the system capacity decreases while it is full. Many complicated factors in networks, such as server downtime, link failure, or competition among pri- oritized applications, can be represented using stochastic ca- pacity models. For example, in a priority service discipline, higher-priority applications may have pre-emptive priority over low-priority applications. We can use a stochastic ca- pacity model to represent the resource availability for low- priority applications. There have been several prior studies for buffered and un- buffered systems that involve the change of server capacity, either implicitly or explicitly. Among them are the unreliable server system, where servers have downtime and later recover [12] [13] [14]. A recent development is performability mod- elling [6] [11] [18], which accounts for both system perfor- mance and system availability. For mobile users using cell phones and mobile devices, mobility leads to many handoff calls. To provide uninterrupted service, certain channels are reserved for handoff only [1]. Hence the number of channels available for new calls may vary. Mobile users access sys- tems by wireless/cellular connections as in CDMA, where interference from neighbouring cells can severely limit the number of calls accepted by a base station. Hence whether the environment is quiet or noisy contributes to capacity fluc- tuations (see [9] and the references therein). The impact of data calls on the capacity of a CDMA multi-service system was evaluated in [19]. The concept of stochastic capacity has been recently proposed for studying the impacts of capacity fluctuation [17]. Due to the complicated nature of the issue, performance was evaluated mainly through simulation. In the infinite buffer case, there is no loss, hence we call it a pure delay system. For a pure delay system, there have been a couple of studies [2] [10] dedicated to the delay performance in a so-called perturbed system, i.e., a small fraction of chan- nels can be taken away to accommodate prioritized traffic. If the system is unbuffered, we have a pure loss system. We assume no buffer, hence a loss system. Loss systems behave quite differently from delay systems. In the stochastic capacity queue, dropping also has an impact on the system performance. As far as we know, this has not been studied in the literature. Some system input parameters, such as the ratio of the load to the mean capacity, and the fluctuation timescale of server capacity (i.e., how frequently the capacity changes relative to the service rate), have major influences on performance. The effects of these factors (e.g.,