The MAP/M/1/K type ticket queue is analysed. Arriving users obtain a ticket for service but may balk the system with the probability depending on the queue of tickets ahead of him/her. Irrespective of joining or balking, the ticket issued for the user remains in the ticket buffer. Also, the waiting user can abandon the system during the waiting time, but his or her ticket remains in the buffer. Users are served in the order of their tickets. The server is unaware about the presence of users in the system and spends some time for his/her service even the respective user already left the system. Ticket queuing systems describe the wide range of real world system. The stationary distribution of the considered system is computed. Numerical illustrations are presented.

A mathematical model is proposed for the operation of a cell in a mobile communication network with moving users. The cell is divided into several zones distinguished by the strength of the signal and, consequently, by the transmission rate. The process of users activation in various zones is defined by the marked Markovian arrival process. After activation, a user can move and transit to other zones or to another cell. The service rate of an arbitrary user depends on the zone where the user is currently located and the total number of active users in the cell. When the total bandwidth required by all active users exceeds the bandwidth of the base station, a proportional reduction of the bitrate provided to each user (bandwidth sharing) is applied. The key performance indicators of the system are computed, and illustrative numerical examples are presented.

The problem of performance evaluation of a wireless sensor node with energy harvesting is formulated as the problem of analysis of the stationary distribution of a single-server queueing system with two finite buffers to which flows of customers and energy units arrive. A unit of energy is required for service of a customer. If energy is not available, service is terminated. To account realistic situations when the parameters of the system can fluctuate, it is assumed that the system operates in a random environment which is defined by the finite state Markov chain. Such fluctuations are possible due to variation of the intensity of signals generation in the sensor node or the change of weather conditions. Under the fixed state of the random environment, arrivals of energy and customers are modelled by stationary Poisson arrival flows and service times have an exponential distribution. Customers in the buffer may be impatient and leave the system after exponentially distributed time. Intensities of the arrival processes, service and impatience immediately change their values at the moments of the jumps of the random environment. The stationary distribution of the system states and the main performance measures of the system are calculated.

A novel multi-server queue with heterogeneous customers is formulated and analyzed as the model of operation of a cell of a mobile communication network. We assume that the cell is divided into zones depending on signal quality. The type of a customer corresponds to a zone in which this customer is currently situated and the rate of the customer's service depends on his/her type. During service, the customer may transit to another zone or terminate service (e.g., owing to poor service quality or departure from the cell). The stationary distribution of the system states and the key performance measures of the system are computed. Numerical results are presented.