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We consider a generic deterministic time-invariant fluid model of a polling system, where several buffers (queues) of infinite sizes receive constant rate inflows of jobs from outside the system and share a common source of service (a finite capacity server). The server can serve at most one buffer at a time and has to switch among buffers from time to time; any switch consumes a nonzero switch-over period. With respect to the long-run maximal scaled work in progress (wip) performance metric, near optimality of periodic scheduling and service protocols is established: The optimum can be furnished by such a protocol up to as small error as desired. To prove this, a special class of protocols is introduced, which prescribe to serve any buffer at the maximal rate until its size reduces to a pre-specified percent of its size at the beginning of the visit. It is also shown that the exhaustive policy is optimal for any buffer whose service at the maximal rate implies reduction in the scaled wip.

A generic time-invariant polling system is modeled as a deterministic hybrid dynamical system in the form of a fluid fabrication facility. The system consists of finitely many infinite size buffers receiving constant-rate inflows from outside the system and a single source of service (finite capacity server). The server can withdraw the buffer’s content but is able to serve at most one buffer at a time, and has to switch among them from time to time, with any switch consuming a nonzero switch-over period. With respect to the long-run maximal scaled wip (work in progress) performance metric, sufficiency of periodic control protocols is established: It is shown that the deepest optimum (that is over all processes in the system, irrespective of their genesis, initial state, and features) is furnished by such a protocol with as high precision as desired. Moreover, sufficiency of special periodic control protocols is established. These protocols prescribe to serve any buffer at the maximal rate until its size reduces to a pre-specified percent of its initial size at the beginning of the visit. This percent is set to be zero for any buffer such that its service at the maximal rate implies reduction of the scaled wip. This is related to another result of the paper that shows optimality of the exhaustive policy for such buffers.

Derivatives of phaeosphaeride A (PPA) were synthesised and characterised; then anti-cancer studies were carried out on the A549 cancer cell line. It was found that the acetyl derivative (compound 3) displayed comparable in vitro cytotoxicity to that of PPA (EC50=49±7 μM and EC50=46±5 μM, respectively), while chloroacetyl derivative 6 (EC50=33±7 μM) was found to have better efficacy towards the A549 cancer cell line.

The herein synthesized 7-(4-methylphenyl)thiomethyl and 7-morpholylmethyl derivatives of natural phaeosphaeride A have lower cytotoxic activity towards the human lung adenocarcinoma A549 cell line compared to phaeosphaeride A. The presence of exocyclic C=C bond and N–OMe group in such compounds is suggested to be a factor in their antitumor activity.