Formulae required for accurate approximate calculation of transition probabilities of embedded Markov chain for single-server queues of the GI/ M/1,GI/M/1/K,M/G/1,M/G/1/K type with heavy-tail lognormal distribution of inter-arrival or service time are given.

In this letter, we present quasi-Jacket block matrices over GF(2), i.e., binary matrices which all are belong to a class of cocyclic matrices. These matrices are may be useful in digital signal processing, CDMA, and coded modulation. Based on Circular Permutation Matrix (CPM) cocyclic quasi-Jacket block low-density matrix is introduced in this letter which is useful in coding theory. Additionally, we show that the fast algorithm of quasi-Jacket block matrix.