Two Unordered Queues

A special customer must complete service from two servers in series, in either order, each with an M/M/1 queueing system. It is assumed that the two queueing system lengths are independent with initial numbers of customers a and b at the instant when the special customer arrives. We find the expected total time (ETT) for the special customer to complete service. We show that even if the interarrival and service time parameters of two queues are identical, there exist examples (specific values of the parameters and initial lengths) for which the special customer surprisingly has a lower expected total time to completion by joining the longer queue first rather than the shorter one.Comment: Presented at AMMCS 2011 Conference, July 25, 201

Double pion production in NNNN and NˉN\bar{N}N collisions

With an effective Lagrangian approach, we give a full analysis on the $NN \to NN\pi\pi$ and $\bar{N}N\to \bar{N}N\pi\pi$ reactions by exploring the roles of various resonances with mass up to 1.72 GeV. We find large contributions from $\Delta$, $N^*(1440)$, $\Delta(1600)$ and $\Delta(1620)$ resonances. Our calculations also indicate sizeable contributions from nucleon poles for the energies close to the threshold. A good description to the existing data of different isospin channels of $NN\to NN\pi\pi$ and $\bar{N}N\to \bar{N}N\pi\pi$ for beam energies up to 2.2 GeV is reached. Our results provide important implications to the ABC effect and guildlines to the future experimental projects at COSY, HADES and HIRFL-CSR. We point out that the \={P}ANDA at FAIR could be an essential place for studying the properties of baryon resonances and the data with baryon and anti-baryon in final states are worth analyzing.Comment: Invited plenary talk at the 11th International Workshop on Meson Production, Properties and Interaction (MESON2010), 10-15 June, 2010, Krakow, Polan