Many applications need to work with several FIFO queues located in a common memory space. Various software or hardware solutions are used to this end [4, 7, 8]. In [8] the problem was formulated for building a mathematical model of the process of working with several FIFO queues in shared memory, where insertion of an item in the queue is allowed on an odd step of the discrete time, and deletion operations – onanevenstep.Theprobabilitiesoftheoperationsareknown.In[5]amathematical model of this process for the number of queues n =2 was proposed, and the problem of optimal partitioning of the shared memory between the two FIFO queues in the case of successive cyclic representation was dealt with. In this paper we construct a mathematical and a simulation models of the process of working with two queues, when they move around a circle, one after another [9].