M-history without the M

M m m Queue with Balking, Reneging and Additional Servers

In this paper, we consider a multi-server queuing system in which additional servers are allowed for a longer queue to reduce the customer’s balking and reneging behavior. The customers are assumed to arrive in Poisson fashion and their service- times follow exponential distribution. The number of servers in long run depends on the queue-length. We obtain equilibrium queue size distribution. Th...

Ideals without Ccc and without Property (m)

We prove a strong version of a theorem of Balcerzak-RoslanowskiShelah by showing, in ZFC, that there exists a simply definable Borel σ-ideal for which both the ccc and property (M) fail. The proof involves Polish group actions. Definition. A Borel ideal is an ideal I on a Polish space X with the following property: for all A ∈ I, there exists a Borel subset B of X such that A ⊂ B and B ∈ I. We ...

مطالعه شونیت های کروماتی M M (Cro ) 6،H O M = NH ,Rb ,Cs ,…, M =Mg ,Ni ,…

M M m K Queue With Additional Servers and Discouragement (RESEARCH NOTE)

Waiting in long queue is undesirable due to which in some practical situations customers become impatient and leave the system. In such cases providing additional servers can reduce long queue. This investigation deals with multi-server queueing system with additional servers and discouragement. The customers arrive in poisson fashion and are served exponentially by a pool of permanent and addi...

$(m,n)$-algebraically compactness and $(m,n)$-pure injectivity

In this paper‎, ‎we introduce the notion of $(m,n)$-‎algebr‎aically compact modules as an analogue of algebraically‎ ‎compact modules and then we show that $(m,n)$-algebraically‎ ‎compactness‎ ‎and $(m,n)$-pure injectivity for modules coincide‎. ‎Moreover‎, ‎further characterizations of a‎ ‎$(m,n)$-pure injective module over a commutative ring are given‎.