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2 Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2 Tikhonenko O.

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Processor sharing queueing systems with non-homogeneous customers

Tikhonenko O.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2010

Vol. 15

149--162

We investigate processor sharing queueing systems with non-homogeneous customers having some random space requirements. Such systems have been used to model and solve various practical problems occurring in the design of computer or communicating systems. The above non-homogenity means that each customer (independently of others) has some random space requirement and his length (or amount of work for his service) generally depends on the space requirement. In real systems, a total sum of space requirements of customers presenting in the system is limited by some constant value (memory capacity) V > 0. We estimate loss characteristcs for such a system using queueing models with unlimited memory space.

Classical and non-classical processor sharing systems with non-homogeneous customers

Tikhonenko O.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2009

Vol. 14

133-150

We discuss a processor sharing system with non-homogeneous customers. There are resources of two types for their service: 1) resource of the first type is discrete, there are N units (servers) of the resource; 2) resource of the second type (capacity) is not-necessary discrete. The type of a customer is defined by the amount of first type resource units which is used for the customer service. Each customer is also characterized by some random capacity or some amount of the second type resource which is also used for his service. The total capacity of customers present in the system is limited by some value V >0, which is called the memory volume of the system. The customer capacity and length (the work necessary for service) are generally dependent. The joint distribution of these random variables also depends on the customer type. For such systems we determine the stationary distribution of the number of customers of each type present in the system and stationary loss probabilities for each type of customers.