4 research outputs found
Product form solution for exponential G-networks with dependent service and completion of service of killed customers
No full textDynamic routing, Communication networks, Mutiobjective Optimisation, Heuristics,
Product form solution for g-networks with dependent service
No full textWe consider a G-network with Poisson flow of positive customers. Each positive customer entering the network is characterized by a set of stochastic parameters: customer route, the length of customer route, customer volume and his service length at each route stage as well. The following node types are considered:
(0) an exponential node with c. servers, infinite buffer and FIFO discipline;
(1) an infinite-server node;
(2) a single-server node with infinite buffer and LIFO PR discipline;
(3) a single-server node with infinite buffer and PS discipline. Negative customers arriving at each node also form a Poisson flow. A negative customer entering a node with k customers in service, with probability Ilk chooses one of served positive customer as a "target". Then, if the node is of a type 0 the negative customer immediately "kills" (displaces from the network) the target customer, and if the node is of types 1-3 the negative customer with given probability depending on parameters of the target customer route kills this customer and with complementary probability he quits the network with no service. A product form for the stationary probabilities of underlying Markov process is obtained
First passage times in M2 [X] | G | 1 | R queue with hysteretic overload control policy
No full textOne of the reported approaches towards the solution of overload problem in networks of SIP servers is the implementation of multi-level hysteretic control of arrivals in SIP servers. Each level, being the parameter of the policy, specifies operation mode of SIP server i.e. it implicitly indicates what SIP server must do with the arriving packets. The choice of parameters' values is not guided by standards and is usually left for the network owner. In general, all operation modes of the considered policy can be grouped into two groups: normal mode (when all arriving packets are accepted) and congested mode (when part or all arriving packets are being dropped). Such grouping may serve as the criteria for choosing parameters' values of the policy: pick those values which minimize SIP server sojourn time in congested mode. In this short note we propose some analytical results which facilitate the solution of stated minimization problem. The considered mathematical model of SIP server is the queueing system M2[X]|G|1|R with batch arrivals and bi-level hysteretic control policy, which specifies three operation modes: normal (customers both flows are accepted), overload (only customers from one flow are accepted), discard (customers from both flows are blocked/lost)). The switching between modes can occur only on service completions. Analytical method allowing computation of stationary sojourn times in different operation modes (as well as first passage times between modes) is presented in brief. Numerical example is given. © 2016 Author(s)
First passage times in M2 [X] | G | 1 | R queue with hysteretic overload control policy
No full textOne of the reported approaches towards the solution of overload problem in networks of SIP servers is the implementation of multi-level hysteretic control of arrivals in SIP servers. Each level, being the parameter of the policy, specifies operation mode of SIP server i.e. it implicitly indicates what SIP server must do with the arriving packets. The choice of parameters' values is not guided by standards and is usually left for the network owner. In general, all operation modes of the considered policy can be grouped into two groups: normal mode (when all arriving packets are accepted) and congested mode (when part or all arriving packets are being dropped). Such grouping may serve as the criteria for choosing parameters' values of the policy: pick those values which minimize SIP server sojourn time in congested mode. In this short note we propose some analytical results which facilitate the solution of stated minimization problem. The considered mathematical model of SIP server is the queueing system M2[X]|G|1|R with batch arrivals and bi-level hysteretic control policy, which specifies three operation modes: normal (customers both flows are accepted), overload (only customers from one flow are accepted), discard (customers from both flows are blocked/lost)). The switching between modes can occur only on service completions. Analytical method allowing computation of stationary sojourn times in different operation modes (as well as first passage times between modes) is presented in brief. Numerical example is given. © 2016 Author(s)
