This paper, proposes an analytical method for the resource allocation and admission control of traffic flows with statistical Quality-of-Service (QoS) guarantees in a Static Priority service discipline, in the case of both isolated nodes and end-to-end paths comprising multiple schedulers. The statistical QoS targets for each service class are expressed in terms of a delay bound and delay violation probability. Moreover, we assume that traffic admits a linear variance envelope; therefore, the method accounts for Leaky-Bucket-regulated traffic, for general Markov-Modulated Poisson Process sources and Markov-Modulated Fluid Process sources and, in general, to the wide class of sources for which the variance of the cumulative generated traffic can be upper bounded by a linear function of time. Under these assumptions, the resource allocation problem is solved analytically by deriving the closed-form expression of the minimum capacity to be allocated in the network in order to guarantee concurrently the QoS of all traffic flows across all service priorities. Moreover, the closed-form analytical solution of the admission control problem is obtained by deriving the expression of the maximum number of flows that is possible to accept, in all priority levels, knowing the link capacity, with differentiated statistical QoS constraints on delay for each priority level. Furthermore, by exploiting the bounded-variance network calculus, a novel framework for the calculation of statistical end-to-end delay bounds, we iterate our formulas, derived for the isolated node, to multi-node paths and, in turn, we provide analytical closed forms for the performance evaluation of end-to-end delay.