Error Analysis of Multiservice Single-Link System Studies Using Linear Approximation Model C. Aswakul Department of Electrical Engineering Faculty of Engineering Chulalongkorn University Bangkok, 10330, Thailand Email: chaodit.a@chula.ac.th J. Barria Department of Electrical and Electronic Engineering Imperial College London South Kensington Campus London, SW7 2AZ, United Kingdom Email: j.barria@ic.ac.uk Abstract— This paper presents an error analysis of the linear approximation model in a multiservice single-link system with nonlinear equivalent capacity. Two types of error measures have been proposed, namely, the mean error and probabilistic error bounds. Derivation of these error measures reveals that the linear approximation model has two main error sources, i.e., the nonlinearity in equivalent capacity and the fluctuation of system dynamics at the mean operating point. In addition, given the product-form solution of the system with the complete sharing policy, a numerical procedure is derived to facilitate the calculation of proposed error measures. This procedure requires both the time and space complexity of O(Ck), where C is the link capacity and k is the number of call types. Hence, these error measures can be efficiently computed in parallel to all the main system performance parameters (call blocking probabilities and mean revenue rates). I. I NTRODUCTION One of the major challenges in communication networking is to find the efficient mechanisms that can provide the quality of service (QoS) for a broad range of applications. To deal with the services with greatly different characteristics, various forms of service separation have been proposed (see, e.g., [1], [2], [3]). The underlying idea of service separation is that only ATM cell or IP packet streams from the same service are allowed to be statistically multiplexed. At a switch or router, a separate buffer is thus allocated to store cells or packets from each service. The QoS provision for each buffer (i.e., loss rate, delay and jitter) can then be facilitated by a weighted round robin or weighted fair queueing scheduler and an appropriate assignment of the scheduling weights. For dynamic service separation (also called service sepa- ration with dynamic partitions in [1]), the scheduling weight for a given buffer i is made directly proportional to G i (n i ), which denotes the equivalent capacity (known as the capacity function in [1]) associated with the buffer i. This equivalent capacity G i (n i ) is the minimum amount of link capacity needed to achieve the QoS guarantee for buffer i when n i connections are being served at the buffer. Therefore, to achieve the QoS guarantee for all the buffers i ∈{1,...,k} that share the same link with capacity C, the number of ongoing connections n i for all i must satisfy the capacity requirement constraint ∑ k i=1 G i (n i ) ≤ C. Under service separation, it is worth noting that G i (·) depends on n i only, and not n j (j = i). Further, to reflect the economies of scale in statistically multiplexing cell or packet streams, it is known that G i (n i ) monotonically increases with decreasing slope as n i increases [4], [5]. For instance, given the on-off source multiplexing model, the stationary Gaussian approximation [5] results in G i (n i )= α i n i + β i √ n i . Therefore, we generally have to cope with a nonlinear equivalent capacity. In the past, given the dynamic service separation with nonlinear equivalent capacity, a few QoS mechanisms have been proposed. For call admission control (CAC), the complete sharing policy has been analyzed [6] in terms of call blocking probabilities of different services. This CAC analysis is then extended to the scenarios of trunk reservation policy [7] to investigate the fairness and prioritization in allocating the link capacity to different services. For network routing, a generalized dynamic alternative routing has been formulated and analyzed in terms of the lower/upper bounds for the mean network revenue rates [8]. The major concept used in solving all the formulated analytical models in [6]–[8] is called the linear approximation model, whose principle is to convert the analytical models from the nonlinear domain of equivalent capacity into an approximated linear domain. Consequently, the efficient nu- merical techniques in the linear domain can then be employed to reduce the involved computational complexity. Efficient numerical techniques are desirable because they need to be repeatedly invoked in network dimensioning procedures. How- ever, the previous studies have only provided empirical inves- tigation on the applicability of linear approximation model. Theoretical error analysis is still needed and becomes the main subject of this paper. In this paper, we theoretically investigate the factors that