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We discuss dynamic system performance evaluation in the river port utilizing queuing models with batch arrivals. The general models of the system are developed. This system is modelled byMX/M/n/mqueue with finite waiting areas and identical and independent cargo-handling capacities. The models are considered with whole and part batch acceptance (or whole and part batch rejections) and the interarrival and service times are exponentially distributed. Results related to the batch blocking probability and the blocking probability of an arbitrary vessel in nonstationary and stationary states have been obtained. Numerical results and computational experiments are reported to evaluate the efficiency of the models for the real system.

Abstract. In this paper we study the structure of closed weakly dense ideals in Privalov spaces N p (1 < p < ∞) of holomorphic functions on the disk D : |z| < 1. The space N p with the topology given by Stoll's metric [21] becomes an F -algebra. N. Mochizuki [16] proved that a closed ideal in N p is a principal ideal generated by an inner function. Consequently, a closed subspace E of N p is invariant under multiplication by z if and only if it has the form IN p for some inner function I. We prove that if M is a closed ideal in N p that is dense in the weak topology of N p , then M is generated by a singular inner function. On the other hand, if Sµ is a singular inner function whose associated singular measure µ has the modulus of continuity O(t (p−1)/p ), then we prove that the ideal SµN p is weakly dense in N p . Consequently, for such singular inner function Sµ, the quotient space N p /SµN p is an F -space with trivial dual, and hence N p does not have the separation property.

We consider the classes M p (1 < p < ∞) of holomorphic functions on the open unit disk 𝔻 in the complex plane. These classes are in fact generalizations of the class M introduced by Kim (1986). The space M p equipped with the topology given by the metric ρ p defined by ρ p(f, g) = ||f − g||p = (∫ 0 2πlogp(1 + M(f − g)(θ))(dθ/2π))1/p, with f, g∈M p and Mf(θ) = sup0⩽r<1 ⁡|f(re iθ)|, becomes an F-space. By a result of Stoll (1977), the Privalov space N p (1 < p < ∞) with the topology given by the Stoll metric d p is an F-algebra. By using these two facts, we prove that the spaces M p and N p coincide and have the same topological structure. Consequently, we describe a general form of continuous linear functionals on M p (with respect to the metric ρ p). Furthermore, we give a characterization of bounded subsets of the spaces M p. Moreover, we give the examples of bounded subsets of M p that are not relatively compact.

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