A random spatial coverage process whose generating point process is homogeneous Poisson, and whose attached random sets are independent and identically distributed, is called a Boolean model. Motivated by Błaszczyszyn et al. [1], distributional and higher moment properties of the size of clumps (connected clusters of overlapping sets) in this model are derived. This provides some complements to the result on the finiteness of the first moment presented in Hall [3]. The key idea is to construct a certain coupling process for a multitype branching process that dominates the clump size.

We obtain the distribution of the length of a clump in a coverage process where the first line segment of a clump has a distribution that differs from the remaining segments of the clump. This result allows us to provide the distribution of the busy period in an M/G/∞ queueing system with exceptional first service, and applications are considered. The result also provides the tool necessary to analyze the transient behavior of an ordinary coverage process, namely the depletion time of the ordinary M/G/∞ system.

The current state of our knowledge of the physical parameters and the chemical composition of dense cores in molecular clouds is discussed. In particular, I summarize what is known about the rate at which molecules condense out on grain surfaces. I discuss in turn: a) dense cores in nearby dust complexes such as Taurus, b) clumps in regions of massive star formation such as Orion and M17, c) hot dense cores near to newly formed O stars such as the Orion-KL hot core and d) the high density condensations which give rise to interstellar masers. Recent work on each of these categories is reviewed with emphasis on the chemical abundance determinations and estimates of the local density and temperature. Particular attention is given to recent work on OH, methanol, and ammonia masers.